5/11 Structure in Expressions

Match each expression to the description shown.

 $2\left(x+1\right)$   

• The sum of a number and two increased by one

• The product of two and a number increased by one

• Two times the difference of a number and one

• Two times the sum of a number and one

A local amusement park charges $20 for an admission fee and $5 for each ride. Jonathon writes an expression to find the total amount he needs to pay for x number of rides.

What does the constant term in the expression represent?

• the number of rides

• the cost per ride

• the admission fee to the park

• the total amount for admission and rides

Shane is selling birdhouses that he makes. The equation for his profit (y) as it relates to the number of birdhouses sold (x) is  $y=15x−75.$  

What does the $15x$ represent in this equation?

• the price for which x birdhouses are sold

• the number of birdhouses Shane needs to sell to break even

• the money Shane spends on supplies for x birdhouses

• the cost of making x birdhouses

Keira is selling lemonade to raise money for a reading program at school. Her profits for selling x glasses of lemonade are represented by the equation $P=0.75x−12.$  

What does the 12 in the equation likely represent?

• the amount of money Keira earns in profit by selling 1 glass of lemonade

• the cost of the materials Keira spends to make the lemonade

• the price Keira charges a customer for each glass of lemonade

• the price Keira charges a customer for 12 glasses of lemonade

Which two expressions are equivalent to $4x^2+20x?$  

•  $4x(x)+4x(5)$  

•  $4x(x+5)$  

•  $4x(5x)$  

•  $5x(x)+5x(4)$  

•  $5x(x+4)$  

• $(2x-3)(2x-3)$

• $(2x-3)(2x+3)$

• $(4x-9)(x-1)$

• $(4x-9)(x+1)$

Which expression is equivalent to $5x^2-14x-24?$  

•  $4(2x+4)(x+5)$  

•  $(5x+6)(x-4)$  

•  $(2x-9)(x-4)$  

•  $(x-6)(5x-4)$  

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Which equation can be used to find the vertex of the quadratic function

 $f(x)=x^2+4x+2?$  

•  $f(x)=(x-2)^2-2$  

•  $f(x)=(x-2)^2+2$  

•  $f(x)=(x+2)^2-2$  

•  $f(x)=(x+2)^2+2$  

What is (are) the zero(s) of the function $y=4x^2-12x+9?$  

•  $x=-\frac{3}{2},\ \frac{3}{2}$  

•  $x=2,\ 3$  

•  $x=\frac{3}{2}$  

•  $x=3$