chapter 4 review pre-calculus. match the graph of a quadratic function with it’s equation below:...
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![Page 1: Chapter 4 Review Pre-Calculus. Match the graph of a quadratic function with it’s equation below: f(x) = x 2 f(x) = -(x+2) 2 +4f(x) = (x+2) 2 -1](https://reader030.vdocuments.mx/reader030/viewer/2022012918/56649ed45503460f94be55cc/html5/thumbnails/1.jpg)
Chapter 4 Review
Pre-Calculus
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Match the graph of a quadratic function with
it’s equation below:
f(x) = x2 f(x) = -(x+2)2+4 f(x) = (x+2)2-1
![Page 3: Chapter 4 Review Pre-Calculus. Match the graph of a quadratic function with it’s equation below: f(x) = x 2 f(x) = -(x+2) 2 +4f(x) = (x+2) 2 -1](https://reader030.vdocuments.mx/reader030/viewer/2022012918/56649ed45503460f94be55cc/html5/thumbnails/3.jpg)
Describe the end behavior of the graph
of each given graph.
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Use the Leading Coefficient Test to determine the end behavior of
the graph of the given polynomial function.
1.) f(x) = -x3 + 4x 2.) f(x) = x4 – 5x2 +4
3.) f(x) = x5 - x
5.) f(x) = -2x4 + 2x2
4.) f(x) = x3 – x2 - 2x
Rise Left, fall right Rise left, rise right
Fall left, rise right Fall left, rise right
Fall left, fall right
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Determine without graphing, the critical
points of each function.
1.) f(x) = (x + 2)2 - 3 2.) f(x) = -x2 + 6x - 8
Min (-2,-3) Max (3,1)
3.) f(x) = 3x3 - 9x + 5 4.) = x3 + 6x2 + 5x
Min (-.47, -1.13)Max (-3.53, 13.12)Pt. of Inflection (-2,6)
Min ( 1, -1)Max (-1, 11)Pt. of Inflection ( 0 , 5)
5.) f(x) = x4 - 10x2 + 9Min ( -√5, -16)Max (0, 9)Min ( √5 , -16)
f’(x) = 2x + 4 f’(x) = -2x + 6
f’(x) = 9x2 - 9 f’’(x) = 18x
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Find the zeros of each polynomial
function.
1.) x2 – 40 = 0 2.) x3 + 4x2 + 4x = 0
3.) x2 + 11x – 102 = 04.) x2 + ¾x + ⅛ = 0
x = 0, -2, -2
x = -17, 6 x = -½, -¼
If you can’t figure it out then use Quadratic Formula
![Page 7: Chapter 4 Review Pre-Calculus. Match the graph of a quadratic function with it’s equation below: f(x) = x 2 f(x) = -(x+2) 2 +4f(x) = (x+2) 2 -1](https://reader030.vdocuments.mx/reader030/viewer/2022012918/56649ed45503460f94be55cc/html5/thumbnails/7.jpg)
Find the zeros of the polynomial function by factoring.
1.) f(x) = x3 + 5x2 – 9x - 451.) f(x) = x3 + 4x2 – 25x - 100
x = 5, -5, -4
![Page 8: Chapter 4 Review Pre-Calculus. Match the graph of a quadratic function with it’s equation below: f(x) = x 2 f(x) = -(x+2) 2 +4f(x) = (x+2) 2 -1](https://reader030.vdocuments.mx/reader030/viewer/2022012918/56649ed45503460f94be55cc/html5/thumbnails/8.jpg)
Which of the following is a rational
zero of
f(x) = –2x5 + 6x4 + 10x3 – 6x2 – 9x
+ 4 1, -3, -2, 4, -1 ????
Remember you could use synthetic division or just do p(x) and see if you get a remainder of ZERO
= 0
So 4 is a factor, the others are not
OR
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Use synthetic division to divide x4 + x3 – 11x2 – 5x +
30 by x - 2 . Then divide by x + 3 Use the result to find
all zeros of f(x).
x2 x C RSo you are left with: x2 - 5
Then all the zeroes are: -3, , 2
![Page 10: Chapter 4 Review Pre-Calculus. Match the graph of a quadratic function with it’s equation below: f(x) = x 2 f(x) = -(x+2) 2 +4f(x) = (x+2) 2 -1](https://reader030.vdocuments.mx/reader030/viewer/2022012918/56649ed45503460f94be55cc/html5/thumbnails/10.jpg)
List all possible rational zeros of
1.) 2.)
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List all possible rational roots, use synthetic division to
find an actual root, then use this root to solve the
equation.
f(x) = 2x4 + x3 – 31x2 – 26x + 24
Hint 4 and -3/2 are roots
2x2 + 6x – 4
USE QUADRATIC FORMULA!!!
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Find the number of possible
positive, negative, and imaginary
zeros of: 2,0 positive roots
0 negative roots
P N IP N I
P N IP N I
2
0
0
0
0
2
1 positive root
3,1 negative roots
1
1
3
1
0
2
3,1 positive roots
1 positive root3
1
1
1
0
2
3,1 positive roots
2,0 positive roots
3311
2020
0224
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Use the given root to find the
solution set of the polynomial
equation.p(x) = x4 + x3 – 7x2 – x + 6GIVEN -3 IS A ROOT
Then we can find the rest by factoring:
So the roots are:-3, -1, 1, and 2
![Page 14: Chapter 4 Review Pre-Calculus. Match the graph of a quadratic function with it’s equation below: f(x) = x 2 f(x) = -(x+2) 2 +4f(x) = (x+2) 2 -1](https://reader030.vdocuments.mx/reader030/viewer/2022012918/56649ed45503460f94be55cc/html5/thumbnails/14.jpg)
Which equation represents the graph of
the function? f(x) = 2x2+2x-1f(x) = -x2-3x+4 f(x) = x2+10x-1
![Page 15: Chapter 4 Review Pre-Calculus. Match the graph of a quadratic function with it’s equation below: f(x) = x 2 f(x) = -(x+2) 2 +4f(x) = (x+2) 2 -1](https://reader030.vdocuments.mx/reader030/viewer/2022012918/56649ed45503460f94be55cc/html5/thumbnails/15.jpg)
Approximate the real zeros of each
function.
0.7, -0.7 -2.5
2.3 -0.4 and -2.6
![Page 16: Chapter 4 Review Pre-Calculus. Match the graph of a quadratic function with it’s equation below: f(x) = x 2 f(x) = -(x+2) 2 +4f(x) = (x+2) 2 -1](https://reader030.vdocuments.mx/reader030/viewer/2022012918/56649ed45503460f94be55cc/html5/thumbnails/16.jpg)
Use the given root to find the
solution set of the polynomial
equations
2i 3-iSince 2i is a root, so is -2i
Turn the roots into factors, multiply them together, then use long division
Then factor to find the remaining roots
So the roots are: 2i, -2i, 3, and -4
Since 3-i is a root, so is 3+i
Turn the roots into factors, multiply them together, then use long division
Then factor to find the remaining roots
So the roots are: 3-i, 3+I, 1, and -4
![Page 17: Chapter 4 Review Pre-Calculus. Match the graph of a quadratic function with it’s equation below: f(x) = x 2 f(x) = -(x+2) 2 +4f(x) = (x+2) 2 -1](https://reader030.vdocuments.mx/reader030/viewer/2022012918/56649ed45503460f94be55cc/html5/thumbnails/17.jpg)
Find the vertical asymptotes, if any, of the graph of each
function.
x = -2, x = 2 x = 4
No vertical asymptote x = -7
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Find the horizontal asymptote, if any, of the
graph of
y = 0y = 1
y = 1y = 3x + 3
If a monomial is on bottom then you just break it up.
Otherwise must do long division
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Choose the correct graph for the rational
function