# Lesson 8

Equations and Graphs

• Let’s write an equation for a parabola.

### Problem 1

Classify the graph of the equation $$x^2+y^2-8x+4y=29$$.

A:

circle

B:

exponential curve

C:

line

D:

parabola

### Problem 2

Write an equation that states $$(x,y)$$ is the same distance from $$(4,1)$$ as it is from the $$x$$-axis.

### Problem 3

Select all equations which describe the parabola with focus $$(\text- 1,\text- 7)$$ and directrix $$y=3$$.

A:

$$(x-1)^2+(y-7)^2=(y+3)^2$$

B:

$$(x+1)^2+(y+7)^2=(y-3)^2$$

C:

$$y=\text{-}20(x+1)^2-2$$

D:

$$y=\text{-}20(x+1)^2+2$$

E:

$$y=\text{-}\frac{1}{20}(x+1)^2-2$$

F:

$$y=\text{-}\frac{1}{20}(x+1)^2+2$$

### Problem 4

Parabola A and parabola B both have the $$x$$-axis as the directrix. Parabola A has its focus at $$(3,2)$$ and parabola B has its focus at $$(5,4)$$. Select all true statements.

A:

Parabola A is wider than parabola B.

B:

Parabola B is wider than parabola A.

C:

The parabolas have the same line of symmetry.

D:

The line of symmetry of parabola A is to the right of that of parabola B.

E:

The line of symmetry of parabola B is to the right of that of parabola A.

(From Unit 6, Lesson 7.)

### Problem 5

A parabola has focus $$(5,1)$$ and directrix $$y = \text{-}3$$. Where is the parabola’s vertex?

(From Unit 6, Lesson 7.)

### Problem 6

Select the value needed in the box in order for the expression to be a perfect square trinomial.

$$x^2+7x+\boxed{\phantom{3}}$$

A:

3.5

B:

7

C:

12.25

D:

14.5

(From Unit 6, Lesson 6.)

### Problem 7

Rewrite each expression as the product of 2 factors.

1. $$x^2+3x$$
2. $$x^2-6x-7$$
3. $$x^2+4x+4$$
(From Unit 6, Lesson 5.)

### Problem 8

Suppose this two-dimensional figure is rotated 360 degrees using the vertical axis shown. Each small square on the grid represents 1 square inch. What is the volume of the three-dimensional figure?

(From Unit 5, Lesson 15.)