Solutions for Lesson 10 Practice Questions

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Contents

Examining Parabolas

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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.
Screen Shot 2013-06-24 at 3.41.08 PM.png

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.
Screen Shot 2013-06-24 at 3.54.21 PM.png

Screen Shot 2013-06-24 at 4.00.49 PM.png

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)