Free Printable Chapter 2 Review

1.

Write f(x) in standard form .

f\left(x\right)=x^2-8x+12

a)

$f\left(x\right)=\left(x+4\right)^2-4$

b)

$f\left(x\right)=\left(x-4\right)^2+12$

c)

$f\left(x\right)=\left(x-4\right)^2-4$

d)

$f\left(x\right)=\left(x-4\right)^2+4$

2.

Write the standard form of the quadratic function whose graph is a parabola with the vertex (2, -1) and passes through the point (5, 2).

a)

$f\left(x\right)=\frac{1}{3}\left(x-2\right)^2-1$

b)

$f\left(x\right)=3\left(x-2\right)^2-1$

c)

$f\left(x\right)=\frac{1}{3}\left(x+2\right)^2-1$

d)

$f\left(x\right)=3\left(x+2\right)^2-1$

3.

Describe the left and right hand behavior of the graph of $f\left(x\right)=-3x^3+4x^2-1$

a)

RIses to the left, falls to the right

b)

RIses to the right, falls to the left

c)

Rises to the right, rises to the left

d)

Falls to the right, falls to the left

4.

Find the real zeros of $f\left(x\right)=-2x^3-x^2+x$ algebraically.

a)

0, -1/2, 1

b)

0, 1/2, 1

c)

0, 1/2, -1

d)

1/2, -1

5.

Use long division to find the quotient and remainder for $\frac{3x^4+x^2-1}{x^2-1}$

a)

$3x^2+4x+\frac{3}{x^2-1}$

b)

$3x^2+4+\frac{3}{x^2-1}$

c)

$3x^2-4-\frac{3}{x^2-1}$

d)

$-3x^2+4+\frac{3}{x^2-1}$

6.

Use synthetic division to divide $\left(2x^3+6x^2-14x+9\right)\div\left(x-1\right)$

a)

$2x^2+8x-6\ r3$

b)

$2x^2+10x-4\ r2$

c)

$2x^2-8x-6\ r3$

d)

$2x^2-10x-4\ r3$

7.

True or False, $\left(x-\sqrt{2}\right)$ is a factor of $2x^5-5x^4-8x+20$

a)

True

b)

False

8.

Write $\sqrt{-50}+8$ in simplest standard form.

a)

$8+\sqrt{50}i$

b)

$64+50i$

c)

$8-5\sqrt{2}i$

d)

$8+5\sqrt{2}i$

9.

Simplify $\left(7+10i\right)-\left(1+9i\right)$

a)

$6+19i$

b)

$6+i$

c)

$-83+53i$

d)

$83-73i$

10.

Write $\frac{1-7i}{2+3i}$ in standard form.

a)

$\frac{1}{2}-\frac{7}{3}i$

b)

$-\frac{19}{13}-\frac{17}{13}i$

c)

$-\frac{19}{11}-\frac{17}{11}i$

d)

$\frac{19}{5}+\frac{17}{5}i$

11.

True or false, the zeros of $f\left(x\right)=x^2+4x+10$ are $x=-2\pm\sqrt{14}i$

a)

True

b)

False

12.

Find all the zeros of $f\left(x\right)=x^3-7x^2+18x-24$

a)

4

b)

$4,\ \frac{3\pm\sqrt{15}i}{4}$

c)

$4,\ \frac{3\pm\sqrt{15}i}{2}$

d)

no solution

13.

Write the polynomial $f\left(x\right)=x^3-5x^2-7x+51$ as a product of linear factors.

a)

$\left(x+3\right)\left(x-4-i\right)\left(x-4+i\right)$

b)

$\left(x+3\right)\left(x+4+i\right)\left(x+4-i\right)$

c)

$\left(x+3\right)\left(x+4i\right)\left(x-4i\right)$

d)

$\left(x+3\right)\left(x^2-8x+17\right)$

14.

Find a polynomial with real coefficients that has the given zeros, $x=-6,\ \ x=-i$

a)

$\left(x-6\right)\left(x^2+1\right)$

b)

$\left(x+6\right)\left(x+i\right)\left(x-i\right)$

c)

$\left(x+6\right)\left(x^2+1\right)$

d)

$\left(x+6\right)\left(x+i\right)$

15.

Determine the vertical asymptotes of $\frac{x^2+x-2}{x^2+2x-3}$

a)

$x=3,\ -1$

b)

$x=-3$

c)

$x=1$

d)

$x=-3,\ 1$

16.

Determine the holes of $\frac{x^2+x-2}{x^2+2x-3}$

a)

$x=3,\ -1$

b)

$x=-3$

c)

$x=1$

d)

$x=-3,\ 1$

17.

Identify any horizontal asymptotes of $\frac{x^2+x-2}{x^2+2x-3}$

a)

$y=o$

b)

$x=1$

c)

$y=1$

d)

$x=-3,\ 1$

18.

Find the zeros of $\frac{x^2+x-2}{x^2+2x-3}$

a)

$x=1,\ -2$

b)

$x=1$

c)

$x=-3$

d)

$x=-2$

19.

Determine the y-intercept for $\frac{x^2+x-2}{x^2+2x-3}$

a)

$y=0$

b)

$y=\frac{2}{3}$

c)

$y=-2$

d)

$y=-\frac{2}{3}$

20.

The given function has a slant asymptote. $f\left(x\right)=\frac{2x^2+7x+3}{x+1}$ Find the equation for the slant asymptote.

a)

$y=2x+5$

b)

$y=2x$

c)

$y=x$

d)

$y=2x+2$

Chapter 2 Review

Total questions: 20

Worksheet time: 5hrs 0mins

Similar Resources on Wayground