# Lesson 8

Equations and Graphs

- Let’s write an equation for a parabola.

### Problem 1

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

circle

exponential curve

line

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 \(y=3\).

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

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

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

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

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

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

### 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.

Parabola A is wider than parabola B.

Parabola B is wider than parabola A.

The parabolas have the same line of symmetry.

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

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

### Problem 5

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

### Problem 6

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

**\(x^2+7x+\boxed{\phantom{3}}\)**

3.5

7

12.25

14.5

### Problem 7

Rewrite each expression as the product of 2 factors.

- \(x^2+3x\)
- \(x^2-6x-7\)
- \(x^2+4x+4\)

### 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?