Review Unit 9

Multiple Choice

If the solutions to a quadratic equation are -4 and 6, the equation can be written as which of the following equations?

• (x-4)(x+6)=0

• (x-4)(x-6)=0

• (x+4)(x+6)=0

• (x+4)(x-6)=0

Why?

The signs in the factored form are the opposite of the solutions to the quadratic equation.

Multiple Choice

For a grade: If the solutions to a quadratic equation are -1 and -2, the equation can be written as which of the following equations?

• (x-1)(x+2)=0

• (x-1)(x-2)=0

• (x+1)(x+2)=0

• (x+1)(x-2)=0

Multiple Choice

Which of the following is equivalent to $$\frac{\sqrt{10}}{\sqrt{3}}$$  ?

• $$\frac{\sqrt{30}}{3}$$  

• $$\sqrt{30}$$  

• $$\sqrt{13}$$  

• $$\frac{\sqrt{13}}{3}$$  

Why?

• Multiply by "magic 1" using the denominator over itself

• When roots multiply the radicands get multiplied

• The root on the bottom of the fraction simplifies because it's a perfect square

Multiple Choice

For a grade: Which of the following is equivalent to $$\frac{\sqrt{5}}{\sqrt{2}}$$  ?

• $$\sqrt{10}$$  

• $$\sqrt{7}$$  

• $$\frac{\sqrt{10}}{2}$$  

• $$\frac{\sqrt{7}}{2}$$  

Multiple Choice

A student is solving $$2\left(x-1\right)^2=72$$  . The first thing the student does is divide by 2. They get  $$\left(x-1\right)^2=36$$  . Next, the student will write...

• $$x-1=\pm6$$  

• $$x-1=\pm36$$  

• $$x^2-1=36$$  

• None of the above

Why?

Multiple Choice

For a grade: A student is solving $$4\left(x+3\right)^2=16$$  . The first thing the student does is divide by 4. They get  $$\left(x+3\right)^2=4$$  . Next, the student will write...

• $$x+3=\pm4$$  

• $$x+3=\pm2$$  

• $$x^2+6x+9=4$$  

• None of the above

Multiple Choice

$$18\left(\frac{\sqrt{2}}{\sqrt{12}}\right)$$  is equivalent to which of the following?
I.  $$3\sqrt{6}$$  
II.  $$5\sqrt{6}-2\sqrt{6}$$  
III.  $$\sqrt{54}$$  

• I only

• II only

• I and III only

• I, II, and III

Multiple Choice

For a grade: $$32\left(\frac{\sqrt{5}}{\sqrt{8}}\right)$$  is equivalent to which of the following?
I.  $$8\sqrt{10}$$  
II.  $$2\sqrt{10}+6\sqrt{10}$$  
III.  $$9\sqrt{10}-\sqrt{40}$$  

• I only

• II only

• I and II only

• I, II, and III

Multiple Choice

What are the solutions to $$4\left(x-7\right)^2=64$$  ?

• x=3, x=11

• x=-1, x=15

• $$x=7\pm\sqrt{32}$$  

• $$x=\pm\sqrt{65}$$  

Why?

• Divide both sides by 4

• Take the square root (positive and negative)

• Add 7 to both sides

• Work out both possibilities: 7+4 and 7-4

Multiple Choice

For a grade: What are the solutions to $$3\left(x+2\right)^2=27$$  ?

• x=3, x=9

• x=1, x=-5

• $$x=3\pm\sqrt{27}$$  

• $$x=\pm9$$  

Multiple Choice

Which equation has the same solution as  $$x^2+6x+8=0$$  ?

• $$\left(x-3\right)^2=-8$$  

• $$\left(x-3\right)^2=1$$  

• $$\left(x+3\right)^2=-8$$  

• $$\left(x+3\right)^2=1$$  

Why?

Complete the Square!

Multiple Choice

For a grade: Which equation has the same solution as  $$x^2+2x-5=0$$  ?

• $$\left(x+1\right)^2=6$$  

• $$\left(x+1\right)^2=1$$  

• $$\left(x-1\right)^2=6$$  

• $$\left(x-1\right)^2=1$$  

Multiple Choice

What are the zeros of the equation below?

• -1/2 and 2/3

• -3/4 and 1/4

• -2

• 1/2 and -2/3

Why?

Graph the line on your graphing calculator and use Menu>Analyze Graph>Zero to identify your zeros.

Multiple Choice

Which equation has one real solution?

• $$2x^2+6x+9=0$$

• $$x^2+6x+9=0$$

• $$x^2+6x+3=0$$

• $$x^2+6x+36=0$$

Why?

It's a perfect square trinomial and the discriminant is zero.

Multiple Select

For a grade: When do equations have one solution?

• Perfect Square Trinomials

• Discriminant=0

• Discriminant<0

• Discriminant>0

Why?