# Solutions for Lesson 10 Practice Questions

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Contents

## Examining Parabolas

What are the x -intercepts of this parabola?

(-1, 0) and (5, 0)

What is its y-intercept?

(0, -15)

## What's Allowed?

You saw in the videos that you can simplify -\frac {1}{8}(x-4)(x-24)=0 by multiplying by -8 to get rid of the -\frac {1}{8} . Now consider x(x-4)(x-24)=0 . Can you simply get rid of the factor x like you did with the -\frac {1}{8} ? Pick all the correct answers.

a) Yes, just divide by x .

incorrect

b) Yes, because the solution is x=4 or x=24 .

incorrect

c) No, because you might be dividing by zero, as you don't know what x is.

correct

d) No, because x=0 is a solution, and so if you get rid of it, you lose a solution.

correct

e) No, because the product is zero, so one of the factors must be zero, which means that either x=0 or (x-4)(x-24)=0 .

correct

## Pick the Equation

Write the letter of each graph next to the proper equation.

y=-x(x+4)

B

y=3(x-2)(x+2)

C

y=-(x-8)(x+2)

D

y=x^2+5x

A

## Solving Quadratic Equations

Fill in the missing parts.

## Satisfying Values

Find the values of x that satisfy each equation. Write them in the box, separated by semicolons (;).

a) (2x+3)(x-1)(x+6)=0

(2x+3)(x-1)(x+6)=0

2x+3=0 or x-1=0 or x+6=0

2x=-3 or x=1 or x=-6

x=-\frac {3}{2}

x=-\frac {3}{2}; 1; -6

b) 13(x-7)(\frac {x}{2}+3)=0

13(x-7)(\frac {x}{2}+3)=0

\frac {x}{2}+3=0 or x-7=0

\frac {x}{2}=-3 or x=7

x=-6

x=7; -6

c) -x(4x+8)(x-11)=0

-x(4x+8)(x-11)=0

4x+8=0 or -x=0 or x-11=0

4x=-8 or x=0 or x=11

x=-2

x=0;-2;11

## Equations of Parabolas?

Which of the following equations graph parabolas? Check all that apply.

y=3x+2

no

-8x^2+y=6

yes

y^2=0

no

y+xy-x^2=-14

no

y=\frac {3x^2}{x-1}

no

y+4=-9x^2-3x

yes

x^3+1=y

no

x^{-2}+y=7

no

## Factoring

Factor the greatest common factor out of each expression. Simplify the rest of the expression.

a) 6x^3-6x^2= ?

6x^3-6x^2=6x^2(x-1)

b) 24z^3+12z+12= ?

24z^3+12z+12=12(2z^3+z+1)

c) 3(x+1)+(x+1)(x-2)= ?

3(x+1)+(x+1)(x-2)=(x+1)(x+1)

d) 9xy-12yz+3xy^2z= ?

9xy-12yz+3xy^2z=3y(3x-4z+xyz)

## Intercepts Everywhere!

Find the x- and y- intercepts of each parabola.

a) y=3x^2+2x

x -intercepts:

0=3x^2+2x

0=x(3x+2)

0=3x+2 or 0=x
-2=3x

-\frac {2}{3}=x

The x -intercepts are (0,0) and (-\frac {2}{3}, 0) .

y -intercept:

y=3(0)^2+2(0)

y=0

The y -intercept is (0,0) .

b) y=x^2

x -intercepts:

0=x^2

0=x

The x -intercept is (0,0) .

y -intercept:

y=(0)^2

y=0

The y -intercept is (0,0) .

c) y=(x-6)(x+2)

x -intercepts:

0=(x-6)(x+2)

0=x-6 or 0=x+2

6=x or -2=x

The x -intercepts are (6,0) and (-2,0) .

y -intercept:

y=(0-6)(0+2)

y=-12

The y -intercept is (0,-12) .