#standard form quadratic equation find vertex

[seekergkfan]

The standard form of the quadratic equation is:

The standard form of the quadratic equation is: A. y = a(x – h)2 + k B. y = a(x + h)2 + k C. y = x2 + bx + c D. y = x2 + k (more…) “”

View On WordPress

#standard form of quadratic equation calcu #standard form of quadratic equation class 10 #standard form of quadratic equation examples #standard form of quadratic equation formula #standard form of quadratic equation meaning #standard form of quadratic equation pdf #standard form of quadratic equation ppt #standard form of quadratic equation solver #standard form of quadratic equation worksheet #standard form quadratic equation calculator #standard form quadratic equation find vertex

[saintkevorkian]

Easy way to find the vertex of a parabola?

where (h, k) are vertex coordinates, parabolic equations can be expressed in one of two forms

f(x) = a (x-h)^2 + k

(up/down parabola)

f(x) = a sqrt(x-h) + k

(charm/strange parabola -- jk it's the sideways parabola, or half of it anyway; to create the other half multiply a by -1)

alternatively, when a quadratic equation is written in standard form (ax^2 + bx + c = 0) , x coordinate of vertex is -b/2a

^the proof for this statement lies in the quadratic formula. The quadratic formula gives the x intercepts, or the places where y=0 (see standard form from which the quadratic formula can be derived by completing the square). As you can see, two solutions lie at the distance sqrt(b^2-4ac) from an axis of symmetry which is -b/2a

you can substitute the x value back into the equation at this point to solve for y. (incidentally, if you solve it symbolically, the y coordinate of the vertex is c - (b^2 /4a)

#maths #algebra

[allcalculator]

Interesting queries on the Quadratic formula calculator!

What are the steps to use the quadratic equation calculator?

Allcalculator.net's The quadratic equation is a polynomial with the highest exponent, which should be 2.  The standard form of the quadratic equation is Ax2 + Bx + C = 0.

Here are the steps to use the quadratic equation calculator are:

Enter the coefficients of the equation in the required input fields with the given statements.

Click on the button to solve the quadratic equation to get the exact result

.

In the final steps, you can find the result for the roots of the quadratic equation, which will be displayed in the output fields.

The basic quadratic formula is:

 X = -b ± √b2 – 4ac / 2a

This above formula is used to solve all the quadratic equations where a ≠ 0 with a polynomial order of 2.

ax2 + bx + c = 0

Enter the equation for real and complex roots in the calculator to determine the discriminant (b2 – 4ac), which is less than, greater than or equal to 0.  

When b2 – 4ac = 0, there is no real roots

When b2 – 4ac > 0, there are two real roots

When b2 – 4ac < 0, there are two complex roots

What are the types of quadratic equations?

There are three types of quadratic equations which are discussed below:

Standard form 

It is a quadratic equation which is given by ax^2 + bx + c = 0 

where a, b, and c are constants and x is a variable. 

Vertex form 

The Vertex form of a quadratic equation is given by a*(x - h) ^2 + k

A h and k are constants, and (h, k) is the vertex of the parabola

Factored form

The factored form of a quadratic equation is given by a*(x - r1) (x - r2)

Where a, r1, and r2 are constants and r1 and r2 are the roots or solutions of the quadratic equation

[studyinginstyle]

Take a diagnostic test

There are many SAT books out there with countless SAT practice tests, but in my opinion the College Board practice tests most closely mimic the types of problems on the actual SAT. Try taking a test and correcting it to see where you need the most work, and to get a feel for the layout of the SAT. Then, you can go on to use books from companies like Princeton Review or Applerouth for more practice.

Set a goal

If you have some idea of the colleges you want to go to, do some research to figure out what the average SAT scores are for students who were admitted. Aim for a score in the upper 25th percentile of those students. 

Learn what you don’t know

Many books will walk you through the steps necessary to complete various types of problems. Go through those carefully, and practice the types of problems you recently learned in order to get accustomed to them.

Practice, practice, practice

The best thing to do once you are familiar with all of the types of problems is practice. Try setting a schedule for yourself, whether it’s doing ten problems a day or one reading and one math section per day. Be sure to check every problem and understand what you got wrong. At frequent intervals, take full-length tests and time yourself within the constraints of the actual test. Check your answers and track your progress.  Kahn Academy is also a great resource for online practice problems.

Basic math formulas to know

·      You are provided with a list of geometry formulas—familiarize yourself with them and be sure you know what they mean

·      Review your times tables up to 12x12 (flashcards)

·      Right triangles—multiples of:

o   3, 4, 5

o   5, 12, 13

o   8, 15, 17

o   7, 24, 25

·      Powers: squares up to 20, cubes up to 10, fourths up to 5, powers of 2 up to 2^10

·      Quadratic forms—standard: y = ax^2 + bx + c, vertex: y = a(x – h)^2 + k

·       Quadratic formula: x=​2a​​−b±√​b​2​​−4ac​​​​​

·      Exponential standard form: y = ab^x

·      Equation of a circle: (x – h)^2 + ( y – k )^2 = r^2

·      Other formulas to know 

Reading and Writing Strategies

·      Although there is no longer a vocab section on the SAT, it is still a good idea to do some vocab practice, especially if you feel you don’t have as strong of a vocabulary as you would like to. Consider buying flashcards or using these online ones https://sat.magoosh.com/flashcards/vocabulary

·      Khan Academy describes a five-step active reading method called SQ3R: “Survey, Question, Read, Recite, Review.” Read more about it here 

·      Familiarize yourself with basic grammar rules and standard conventions:

o   tenses (a sentence that changes tenses partway through will likely be incorrect)

o   run-on sentences

o   modifiers

o   subject-verb agreement

o   transitions

o   punctuation

o   find more here

Essay strategies

·      The essay is no longer required in the new SAT, but it is a good choice for someone if you are applying to colleges that require an essay, or if you want to show extra dedication or academic prowess. It is generally highly recommended to opt in for the essay.

·      You will be evaluated with sub-scores out of 4 for three categories: reading, analysis and writing.

·      Read sample essays and pay attention to patterns—what did higher-scoring essays do more of? (https://collegereadiness.collegeboard.org/sample-questions/essay/1)

·      Begin by reading the prompt or the passage carefully and construct a thesis

·      Outline your essay. Be sure all body paragraphs address your thesis.

·      Longer essays generally score higher, but try to make it as dense as possible. It will be obvious if you are using a lot of “filler” sentences and ideas.

·      Leave enough time to edit. Although it’s handwritten, that shouldn’t stop you from going back to make changes. 

Some other useful resources

·      Find a tutor in your area or enroll in an SAT class

·      This explanation of all the different areas of the test from College Board 

·      SAT practice strategies, problems, videos and explanations from Khan Academy 

·      Princeton Review book of 11 different practice tests 

·      Find flashcards for various topics on Quizlet

·      Read a lot from reputable journals or periodicals such as the New York Times 

On the day of the test

Relax! You have done all you can to prepare, so be confident that you can do well. Take deep breaths and try not to get too nervous. Good luck!

#studyinginstyle #study tips #SAT #SAT study tips #SAT studying #SAT resources #studyblr #studying #mine

[slmathblog-blog]

Week 14-20

From December 4th to December 13th, we’ve focused on Quadratic Functions. We’ve looked at the characteristics of a Quadratic Function, as well as learning how to draw the graph of a Quadratic Function.

Here are the comparisons between a Linear Function and a Quadratic Function:

Standard Form: y=mx+b [Linear], y=ax^2+bx+c [Quad]

Degree: All the variables are the first power [Linear], Independent variable (x) is squared in first term. Coeffecient of (a) cannot be equal to 0, otherwise the equation will become linear [Quad]

Graph: Line [Linear], Parabola [Quad]

On December 13th, Ms. Pali-tang was sick and absent on the day, so Mr. Chua instead supervised us. We did a introductory activity on Quadratic Functions of a tunnel design, but I couldn’t really understand how to do it.

On December 15th, I’ve worked on my other work.

On December 17th, we were introduced to our IA, and we were shown videos that could help with our IA.

We’ve entered Winter Break shortly after, and we’ve came back on January 4th (but I’ve came back on January 5th because of health problems).

On January 10th, we’ve reviewed the properties of the Quadratic Function, and we did an activity on investigating Quadratic Functions (finding x and y intercept, vertex and line of symmetry)

January 12th was a free period, and I’ve read the guide for the IA. 

On January 15, we’ve continued the investigation on Quadratic Functions. 

[tutorsof]

MA240 Online Exam 3_05 SCORE 100 PERCENT

Question 1 of 20

5.0 Points

  Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the following rational function.

  f(x) = x/x + 4

      A. Vertical asymptote: x = -4; no holes

    B. Vertical asymptote: x = -4; holes at 3x

    C. Vertical asymptote: x = -4; holes at 2x

    D. Vertical asymptote: x = -4; holes at 4x

  Question 2 of 20

5.0 Points

Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x2 or g(x) = -3x2, but with the given maximum or minimum. Maximum = 4 at x = -2

A. f(x) = 4(x + 6)2 - 4

B. f(x) = -5(x + 8)2 + 1

C. f(x) = 3(x + 7)2 - 7

D. f(x) = -3(x + 2)2 + 4

  Question 3 of 20

5.0 Points

The perimeter of a rectangle is 80 feet. If the length of the rectangle is represented by x, its width can be expressed as:

A. 80 + x.

B. 20 - x.

C. 40 + 4x.

D. 40 - x.

    Question 4 of 20

5.0 Points

Determine the degree and the leading coefficient of the polynomial function f(x) = -2x3 (x - 1)(x + 5).

A. 5; -2

B. 7; -4

C. 2; -5

D. 1; -9

  Question 5 of 20

5.0 Points

40 times a number added to the negative square of that number can be expressed as:

A. A(x) = x2 + 20x.

B. A(x) = -x + 30x.

C. A(x) = -x2 - 60x.

D. A(x) = -x2 + 40x.

  Question 6 of 20

5.0 Points

8 times a number subtracted from the squared of that number can be expressed as:

A. P(x) = x + 7x.

B. P(x) = x2 - 8x.

C. P(x) = x - x.

D. P(x) = x2+ 10x.

  Question 7 of 20

5.0 Points

The difference between two numbers is 8. If one number is represented by x, the other number can be expressed as:

A. x - 5.

B. x + 4.

C. x - 8.

D. x - x.

  Question 8 of 20

5.0 Points

Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.   f(x) = x3 + 2x2 - x - 2

A. x = 2, x = 2, x = -1; f(x) touches the x-axis at each.

B. x = -2, x = 2, x = -5; f(x) crosses the x-axis at each.

C. x = -3, x = -4, x = 1; f(x) touches the x-axis at each.

D. x = -2, x = 1, x = -1; f(x) crosses the x-axis at each.

  Question 9 of 20

5.0 Points

All rational functions can be expressed as f(x) = p(x)/q(x), where p and q are __________ functions and q(x) ≠ 0.

A. horizontal asymptotes

B. polynomial

C. vertical asymptotes

D. slant asymptotes

  Question 10 of 20

5.0 Points

Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x) = -2(x + 1)2 + 5

A. (-1, 5)

B. (2, 10)

C. (1, 10)

D. (-3, 7)

  Question 11 of 20

5.0 Points

Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x2 or g(x) = -3x2, but with the given maximum or minimum. Minimum = 0 at x = 11

A. f(x) = 6(x - 9)

B. f(x) = 3(x - 11)2

C. f(x) = 4(x + 10)

D. f(x) = 3(x2 - 15)2

  Question 12 of 20

5.0 Points

Solve the following polynomial inequality. 3x2 + 10x - 8 ≤ 0

A. [6, 1/3]

B. [-4, 2/3]

C. [-9, 4/5]

D. [8, 2/7]

  Question 13 of 20

5.0 Points

Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. f(x) = -2x4 + 4x3

A. x = 1, x = 0; f(x) touches the x-axis at 1 and 0

B. x = -1, x = 3; f(x) crosses the x-axis at -1 and 3

C. x = 0, x = 2; f(x) crosses the x-axis at 0 and 2

D. x = 4, x = -3; f(x) crosses the x-axis at 4 and -3

  Question 14 of 20

5.0 Points

Find the domain of the following rational function. g(x) = 3x2/((x - 5)(x + 4))

A. {x│ x ≠ 3, x ≠ 4}

B. {x│ x ≠ 4, x ≠ -4}

C. {x│ x ≠ 5, x ≠ -4}

D. {x│ x ≠ -3, x ≠ 4}

  Question 15 of 20

5.0 Points

Find the domain of the following rational function. f(x) = 5x/x - 4

A. {x │x ≠ 3}

B. {x │x = 5}

C. {x │x = 2}

D. {x │x ≠ 4}

  Question 16 of 20

5.0 Points

Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as y and z

A. x = kz; y = x/k

B. x = kyz; y = x/kz

C. x = kzy; y = x/z

D. x = ky/z; y = x/zk

  Question 17 of 20

5.0 Points

Solve the following polynomial inequality. 9x2 - 6x + 1

A. (-∞, -3)

B. (-1, ∞)

C. [2, 4)

D. Ø

  Question 18 of 20

5.0 Points

Based on the synthetic division shown, the equation of the slant asymptote of f(x) = (3x2 - 7x + 5)/x – 4 is:

A. y = 3x + 5.

B. y = 6x + 7.

C. y = 2x - 5.

D. y = 3x2 + 7.

  Question 19 of 20

5.0 Points

Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 2x2, but with the given point as the vertex (5, 3).

A. f(x) = (2x - 4) + 4

B. f(x) = 2(2x + 8) + 3

C. f(x) = 2(x - 5)2 + 3

D. f(x) = 2(x + 3)2 + 3

  Question 20 of 20

5.0 Points

The graph of f(x) = -x3 __________ to the left and __________ to the right.

A. rises; falls

B. falls; falls

C. falls; rises

D. falls; falls

[tutorsof]

MA240 Online Exam 3_05 SCORE 100 PERCENT

Question 1 of 20

5.0 Points

  Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the following rational function.

  f(x) = x/x + 4

      A. Vertical asymptote: x = -4; no holes

    B. Vertical asymptote: x = -4; holes at 3x

    C. Vertical asymptote: x = -4; holes at 2x

    D. Vertical asymptote: x = -4; holes at 4x

  Question 2 of 20

5.0 Points

Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x2 or g(x) = -3x2, but with the given maximum or minimum. Maximum = 4 at x = -2

A. f(x) = 4(x + 6)2 - 4

B. f(x) = -5(x + 8)2 + 1

C. f(x) = 3(x + 7)2 - 7

D. f(x) = -3(x + 2)2 + 4

  Question 3 of 20

5.0 Points

The perimeter of a rectangle is 80 feet. If the length of the rectangle is represented by x, its width can be expressed as:

A. 80 + x.

B. 20 - x.

C. 40 + 4x.

D. 40 - x.

    Question 4 of 20

5.0 Points

Determine the degree and the leading coefficient of the polynomial function f(x) = -2x3 (x - 1)(x + 5).

A. 5; -2

B. 7; -4

C. 2; -5

D. 1; -9

  Question 5 of 20

5.0 Points

40 times a number added to the negative square of that number can be expressed as:

A. A(x) = x2 + 20x.

B. A(x) = -x + 30x.

C. A(x) = -x2 - 60x.

D. A(x) = -x2 + 40x.

  Question 6 of 20

5.0 Points

8 times a number subtracted from the squared of that number can be expressed as:

A. P(x) = x + 7x.

B. P(x) = x2 - 8x.

C. P(x) = x - x.

D. P(x) = x2+ 10x.

  Question 7 of 20

5.0 Points

The difference between two numbers is 8. If one number is represented by x, the other number can be expressed as:

A. x - 5.

B. x + 4.

C. x - 8.

D. x - x.

  Question 8 of 20

5.0 Points

Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.   f(x) = x3 + 2x2 - x - 2

A. x = 2, x = 2, x = -1; f(x) touches the x-axis at each.

B. x = -2, x = 2, x = -5; f(x) crosses the x-axis at each.

C. x = -3, x = -4, x = 1; f(x) touches the x-axis at each.

D. x = -2, x = 1, x = -1; f(x) crosses the x-axis at each.

  Question 9 of 20

5.0 Points

All rational functions can be expressed as f(x) = p(x)/q(x), where p and q are __________ functions and q(x) ≠ 0.

A. horizontal asymptotes

B. polynomial

C. vertical asymptotes

D. slant asymptotes

  Question 10 of 20

5.0 Points

Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x) = -2(x + 1)2 + 5

A. (-1, 5)

B. (2, 10)

C. (1, 10)

D. (-3, 7)

  Question 11 of 20

5.0 Points

Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x2 or g(x) = -3x2, but with the given maximum or minimum. Minimum = 0 at x = 11

A. f(x) = 6(x - 9)

B. f(x) = 3(x - 11)2

C. f(x) = 4(x + 10)

D. f(x) = 3(x2 - 15)2

  Question 12 of 20

5.0 Points

Solve the following polynomial inequality. 3x2 + 10x - 8 ≤ 0

A. [6, 1/3]

B. [-4, 2/3]

C. [-9, 4/5]

D. [8, 2/7]

  Question 13 of 20

5.0 Points

Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. f(x) = -2x4 + 4x3

A. x = 1, x = 0; f(x) touches the x-axis at 1 and 0

B. x = -1, x = 3; f(x) crosses the x-axis at -1 and 3

C. x = 0, x = 2; f(x) crosses the x-axis at 0 and 2

D. x = 4, x = -3; f(x) crosses the x-axis at 4 and -3

  Question 14 of 20

5.0 Points

Find the domain of the following rational function. g(x) = 3x2/((x - 5)(x + 4))

A. {x│ x ≠ 3, x ≠ 4}

B. {x│ x ≠ 4, x ≠ -4}

C. {x│ x ≠ 5, x ≠ -4}

D. {x│ x ≠ -3, x ≠ 4}

  Question 15 of 20

5.0 Points

Find the domain of the following rational function. f(x) = 5x/x - 4

A. {x │x ≠ 3}

B. {x │x = 5}

C. {x │x = 2}

D. {x │x ≠ 4}

  Question 16 of 20

5.0 Points

Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as y and z

A. x = kz; y = x/k

B. x = kyz; y = x/kz

C. x = kzy; y = x/z

D. x = ky/z; y = x/zk

  Question 17 of 20

5.0 Points

Solve the following polynomial inequality. 9x2 - 6x + 1

A. (-∞, -3)

B. (-1, ∞)

C. [2, 4)

D. Ø

  Question 18 of 20

5.0 Points

Based on the synthetic division shown, the equation of the slant asymptote of f(x) = (3x2 - 7x + 5)/x – 4 is:

A. y = 3x + 5.

B. y = 6x + 7.

C. y = 2x - 5.

D. y = 3x2 + 7.

  Question 19 of 20

5.0 Points

Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 2x2, but with the given point as the vertex (5, 3).

A. f(x) = (2x - 4) + 4

B. f(x) = 2(2x + 8) + 3

C. f(x) = 2(x - 5)2 + 3

D. f(x) = 2(x + 3)2 + 3

  Question 20 of 20

5.0 Points

The graph of f(x) = -x3 __________ to the left and __________ to the right.

A. rises; falls

B. falls; falls

C. falls; rises

D. falls; falls

#Business Management #Ashworth #Phoenix #UOP #Assignment

[tutorsof]

Math Assignment-6

Question - 1

Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x2 or g(x) = -3x2, but with the given maximum or minimum. 

Maximum = 4 at x = -2

A. f(x) = 4(x + 6)2 - 4 

B. f(x) = -5(x + 8)2 + 1 

C. f(x) = 3(x + 7)2 - 7 

D. f(x) = -3(x + 2)2 + 4

Question - 2

All rational functions can be expressed as f(x) = p(x)/q(x), where p and q are __________ functions and q(x) ≠ 0.

A. horizontal asymptotes 

B. polynomial 

C. vertical asymptotes 

D. slant asymptotes

Question - 3

8 times a number subtracted from the squared of that number can be expressed as:

A. P(x) = x + 7x. 

B. P(x) = x2 - 8x.

C. P(x) = x - x. 

D. P(x) = x2+ 10x.

Question - 4

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers.

f(x) = 2x4 - 4x2 + 1; between -1 and 0

A. f(-1) = -0; f(0) = 2 

B. f(-1) = -1; f(0) = 1 

C. f(-1) = -2; f(0) = 0 

D. f(-1) = -5; f(0) = -3

Question - 5

"Y varies directly as the nth power of x" can be modeled by the equation:

A. y = kxn. 

B. y = kx/n. 

C. y = kx*n. 

D. y = knx.

Question - 6

Based on the synthetic division shown, the equation of the slant asymptote of f(x) = (3x2 - 7x + 5)/x – 4 is:

A. y = 3x + 5. 

B. y = 6x + 7. 

C. y = 2x - 5. 

D. y = 3x2 + 7.

Question - 7

Write an equation that expresses each relationship. Then solve the equation for y. 

x varies jointly as y and z

A. x = kz; y = x/k 

B. x = kyz; y = x/kz 

C. x = kzy; y = x/z 

D. x = ky/z; y = x/zk

Question - 8

Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the following rational function.

f(x) = x/x + 4

A. Vertical asymptote: x = -4; no holes 

B. Vertical asymptote: x = -4; holes at 3x 

C. Vertical asymptote: x = -4; holes at 2x 

D. Vertical asymptote: x = -4; holes at 4x

Question - 9

Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.

 f(x) = x3 + 2x2 - x - 2

A. x = 2, x = 2, x = -1; f(x) touches the x-axis at each. 

B. x = -2, x = 2, x = -5; f(x) crosses the x-axis at each. 

C. x = -3, x = -4, x = 1; f(x) touches the x-axis at each. 

D. x = -2, x = 1, x = -1; f(x) crosses the x-axis at each

Question - 10

If f is a polynomial function of degree n, then the graph of f has at most __________ turning points.

A. n - 3 

B. n - f 

C. n - 1 

D. n + f

Question - 11

The difference between two numbers is 8. If one number is represented by x, the other number can be expressed as:

A. x - 5. 

B. x + 4. 

C. x - 8. 

D. x - x.

Question - 12

9x2 - 6x + 1

A. (-∞, -3) 

B. (-1, ∞) 

C. [2, 4) 

D. Ø

Question - 13

Solve the following polynomial inequality.

3x2 + 10x - 8 ≤ 0

A. [6, 1/3] 

B. [-4, 2/3] 

C. [-9, 4/5] 

D. [8, 2/7]

Question - 14

Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x2 or g(x) = -3x2, but with the given maximum or minimum.

Minimum = 0 at x = 11

A. f(x) = 6(x - 9) 

B. f(x) = 3(x - 11)2 

C. f(x) = 4(x + 10) 

D. f(x) = 3(x2 - 15)2

Question - 15

Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 2x2, but with the given point as the vertex (5, 3).

A. f(x) = (2x - 4) + 4 

B. f(x) = 2(2x + 8) + 3 

C. f(x) = 2(x - 5)2 + 3 

D. f(x) = 2(x + 3)2 + 3

Question - 16

Find the coordinates of the vertex for the parabola defined by the given quadratic function. 

f(x) = -2(x + 1)2 + 5

A. (-1, 5) 

B. (2, 10) 

C. (1, 10) 

D. (-3, 7)

Question - 17

Determine the degree and the leading coefficient of the polynomial function f(x) = -2x3 (x - 1)(x + 5).

A. 5; -2 

B. 7; -4 

C. 2; -5 

D. 1; -9

Question - 18

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. 

f(x) = x3 - x - 1; between 1 and 2

A. f(1) = -1; f(2) = 5 

B. f(1) = -3; f(2) = 7 

C. f(1) = -1; f(2) = 3 

D. f(1) = 2; f(2) = 7

Question - 19

Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the following rational function.

g(x) = x + 3/x(x + 4)

A. Vertical asymptotes: x = 4, x = 0; holes at 3x 

B. Vertical asymptotes: x = -8, x = 0; holes at x + 4 

C. Vertical asymptotes: x = -4, x = 0; no holes 

D. Vertical asymptotes: x = 5, x = 0; holes at x – 3

Question - 20

The graph of f(x) = -x3 __________ to the left and __________ to the right.

A. rises; falls 

B. falls; falls 

C. falls; rises 

D. falls; falls