IM Unit 7 Review

IM Unit 7 Review

Quadratic Equations

Multiple Select

Select all expressions that are squares of linear expressions.

• $x^2+6x+36$

• $\left(\frac{1}{2}x+4\right)^2$

• $\left(2d+8\right)\left(2d-8\right)$

• $p^2-6p+9$

• $x^2+36$

Multiple Select

 Select all equations that are equivalent to  $x^2+6x=16$ 

•  $x^2+6x+9=0$  

•  $x^2+6x+9=16$  

•  $x^2+6x+9=25$  

•  $\left(x+3\right)^2=0$  

•  $\left(x+3\right)^2=25$  

Multiple Choice

A quadratic function is defined by $f\left(x\right)=x^2-8x-4$                  

Which expression also defines f and best reveals the maximum or minimum of the function?

•  $\left(x-4\right)^2+20$  

•  $x\left(x-8\right)-4$  

•  $\left(x-4\right)^2+12$  

•  $\left(x-4\right)^2-20$  

Fill in the Blanks

Solve the following equation by completing the square:  $x^2-12x=-20$  

x =

 

Either solution to x will be marked correct. 

Fill in the Blanks

Solve the following equation by completing the square: $9x^2+12x+5=10$  

x =

Either solution for x will be marked as correct. Do not put spaces in your answer. 

Fill in the Blanks

Solve the following equation: $4x^2-5x-6=0$  

Either solution of x will be marked correct. Do not put spaces in your answer. 

Multiple Choice

A solution to an equation Jada solved is  $-2+\sqrt{3}$  . She is trying to determine whether that solution is rational or irrational. 

Jada knows that -2 is a rational number and  $\sqrt{3}$   is an irrational number. She also knows that the sum of any two rational numbers is always rational.

If we add 2 to  $-2+\sqrt{3}$  , will the sum be rational or irrational?

• rational

• irrational

Open Ended

Explain why $-2+\sqrt{3}$  cannot be rational. 

When you add two rational numbers together, you should get another rational number.

Adding $-2+\sqrt{3}$  and 2 gives you an irrational number. 

Fill in the Blanks

A community theater uses the function $p\left(d\right)=-4d^2+200d-100$ to model the profit (in dollars) expected in a weekend when the tickets to a comedy show are priced at d dollars each.

 Write and solve an equation to find out the prices at which the theater would earn $1,500 in profit from the comedy show each weekend. 

Either value of d will be marked as correct. 

Open Ended

A community theater uses the function $p\left(d\right)=-4d^2+200d-100$ to model the profit (in dollars) expected in a weekend when the tickets to a comedy show are priced at d dollars each. 
The profit will be $1,500 when d=10 or d=40.
At what price would the theater make the maximum profit, and what is that maximum profit? Show your reasoning.