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?

Quadrilateral on grid with its longest side aligned with a bolded vertical grid line. Longest side is 6 units. Top side is 2. Right side is 3, followed by a diagonal side connecting to the long side.
(From Unit 5, Lesson 15.)