Lesson 1 When and Why We Write Quadratics

Lesson 1 When and Why We Write Quadratics

Multiple Choice

A set of kitchen containers can be stacked to save space. The height of the stack is given by the expression 1.5c+7.6, where c is the number of containers.

Find the height of a stack made of 8 containers.

• 16.9 units

• 19.6 units

• 14.5 units

• 0.26 units

Fill in the Blanks

A set of kitchen containers can be stacked to save space. The height of the stack is given by the expression 1.5c+7.6, where c is the number of containers.

A tower made of all the containers is 40.6 cm tall. How many containers are in the set?

Write the numeric answer only. (Just write the number)

Open Ended

A set of kitchen containers can be stacked to save space. The height of the stack is given by the expression 1.5c+7.6, where c is the number of containers.

Noah looks at the equation and says, “7.6 must be the height of a single container.” Do you agree with Noah? Explain your reasoning.

Multiple Select

Select all values of x that are solutions to the equation (x−5)(7x−21)=0.

• -7

• -5

• -3

• 3

• 5

Open Ended

Which expression makes it easier to find f(0),  (5x-20)(6x+3) or  $30x^2-105x-60$  .  Explain your reasoning.

Fill in the Blanks

The expressions 

 $30x^2-405x-60$  and (5x−20)(6x+3) define the same function, f. Find f(0).

Open Ended

 $30x^2-105x-60\ or\ \left(5x-20\right)\left(6x+3\right)$  

Which expression makes it easier to find the values of x that make the equation f(x)=0 true?

Multiple Choice

 $30x^2-105x-60\ and\ \left(5x-20\right)\left(6x+3\right)$  

define the same function.  Find the values of x that make f(x)=0.

• x=4, x=0.5

• x=4 x=-0.5

• x=-4, x=2

• x=-4 x=-2,

Multiple Select

A band is traveling to a new city to perform a concert. The revenue from their ticket sales is a function of the ticket price, x, and can be modeled with (x−6)(250−5x).

What are the ticket prices at which the band would make no money at all?

• $6

• $0

• $50

• $-6

Fill in the Blanks

What is the value of h(3)?

Open Ended

Explain why h(0)=h(8).

Fill in the Blanks

What value of t gives h(t)=252? Type only the numeric answer. (Only type the number.)