Free Printable Zeros and Ellipses Review

1.

Find all zeros of f(x) = x³- 5x²- 2x + 24, given x = - 2 is a zero.

a)

x = -2, 1, 0

b)

x = -2, -3, -4

c)

x = -2, 4, 3

d)

x = 0

2.

The zeros of f(x) are x = -2, 3, and 4. Write f(x) as a product of linear factors.

f(x) = x³- 5x²- 2x + 24

a)

(x - 2)(x - 3)(x - 4)

b)

(x - 2)(x + 3)(x + 4)

c)

(x + 2)(x - 3)(x - 4)

d)

(x + 2)(x + 3)(x + 4)

3.

Find ALL zeros of f(x) = x³ - 2x² + 9x - 18, given x = 2 is a zero.

a)

x = 2, 3i, -3i

b)

x = -2, 3, -3

c)

x = 2, 3, -3

d)

x = -2, 3i, -3i

4.

The zeros of f(x) are x = 2, 3i, and -3i. Write f(x) as a product of linear factors.

f(x) = x³ - 2x² + 9x - 18

a)

(x - 2)(x - 3i)(x + 3i)

b)

(x + 2)(x - 3i)(x + 3i)

c)

(x - 2)(-3i)(3i)

d)

(x + 2)(-3i)(3i)

5.

Find all the zeros of this polynomial, given x = -1 is a solution.

g(x) = x³ + 11 x² + 44x + 34

a)

x = -1,

-5 + 3i,

-5 - 3i

b)

x = -1,

5 + 3i,

5 - 3i

c)

x = 1,

-5 + 3i,

-5 - 3i

d)

x = -1,

-10 + 6i,

-10 - 6i

6.

The zeros of g(x) are x = -1, -5 + 3i, and -5 - 3i. Write g(x) in factored form.

g(x) = x³ + 11 x² + 44x + 34

a)

(x + 1)(x + 5 - 3i)(x + 5 + 3i)

b)

(x + 1)(x - 5 - 3i)(x - 5 + 3i)

c)

(x + 1)(x + 5 + 3i)(x - 5 - 3i)

7.

The major axis is:

a)

either "a" or "b", whichever is the shorter axis.

b)

either "a" or "b", whichever is the longer axis.

c)

always "a", the axis in the x-direction.

d)

always "b", the axis in the y-direction.

8.

The minor axis is:

a)

either "a" or "b", whichever is the shorter axis.

b)

either "a" or "b", whichever is the longer axis.

c)

always "a", the axis in the x-direction.

d)

always "b", the axis in the y-direction.

9.

For this equation of an ellipse, what is the value of a?

a)

0

b)

1

c)

7

d)

49

10.

Given the equation of the ellipse, what is a?

a)

8

b)

11

c)

64

d)

121

11.

Given the equation of the ellipse, what is b?

a)

8

b)

11

c)

64

d)

121

12.

Identify both a and b.

a)

a=25 b=4

b)

a=4 b=25

c)

a=2 b=5

d)

a=5 b=2

13.

What is the center of the shifted ellipse?

a)

(0,0)

b)

(-3,1)

c)

(1,-3)

d)

(3,-1)

14.

What is the center of the given equation?

a)

(4, 3)

b)

(-4, -3)

c)

(-4, 3)

d)

(4, -3)

15.

What is the value of b?

a)

3

b)

5

c)

6

d)

10

16.

Find the standard equation of the given ellipse

a)

b)

c)

d)

17.

What is the equation of the given graph?

a)

$\frac{x^2}{7}+\frac{y^2}{6}=1$

b)

$\frac{x^2}{14}+\frac{y^2}{12}=1$

c)

$\frac{x^2}{49}+\frac{y^2}{36}=1$

d)

$\frac{x^2}{36}+\frac{y^2}{49}=1$

18.

The graph of an ellipse is shown. Which equation represents this ellipse?

a)

$\frac{\left(x-1\right)^2}{16}+\frac{\left(y+1\right)^2}{36}=1$

b)

$\frac{\left(x-1\right)^2}{36}+\frac{\left(y+1\right)^2}{16}=1$

c)

$\frac{\left(x+1\right)^2}{16}+\frac{\left(y-1\right)^2}{36}=1$

d)

$\frac{\left(x+1\right)^2}{36}+\frac{\left(y-1\right)^2}{16}=1$

19.

The graph of an ellipse is shown. Which equation represents this ellipse?

a)

$\frac{\left(x+3\right)^2}{9}+\frac{\left(y-2\right)^2}{25}=1$

b)

$\frac{\left(x-3\right)^2}{25}+\frac{\left(y+2\right)^2}{9}=1$

c)

$\frac{\left(x-3\right)^2}{9}+\frac{\left(y+2\right)^2}{25}=1$

d)

$\frac{\left(x+3\right)^2}{25}+\frac{\left(y-2\right)^2}{9}=1$

20.

Is the graph of this ellipse horizontal or vertical?

a)

b)

c)

not enough information

21.

Which of the following is the graph of $\frac{\left(x+3\right)^2}{4}+\frac{\left(y+1\right)^2}{9}=1$

a)

b)

c)

d)

22.

What is PF + PG equal to?

a)

2a

b)

2b

c)

2a or 2b, whichever is longer

d)

2a or 2b, whichever is shorter

23.

What is PF + PG for this equation?

a)

50

b)

8

c)

4

d)

10

24.

What is PF + PG for this graph?

a)

6

b)

3

c)

2

d)

4

25.

Suppose the foci of an ellipse are (0, -3) and (0, 3).

Which direction will the ellipse go?

a)

b)

26.

Suppose PF + PG = 26 and the foci are (12, 0) and (-12, 0).

What is the major axis length?

a)

a = 13

b)

b = 13

c)

a = 52

d)

b = 52

27.

Suppose PF + PG = 26 and the foci are (0, 12) and (0, -12).

What is the major axis length?

a)

a = 13

b)

b = 13

c)

a = 52

d)

b = 52

Zeros and Ellipses Review

Total questions: 27

Worksheet time: 7hrs 31mins

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