IM Alg1.7.4 Practice: Solving Quadratic Equations with the Zero Product Property

If the equation  is true, which statement is also true according to the zero product property?

What are the solutions to the equation ?

Consider the expressions and . Show that the two expressions define the same function.

Kiran saw that if the equation is true, then, by the zero product property, either is 0 or is 0. He then reasoned that, if is true, then either is equal to 72 or is equal to 72.  Explain why Kiran’s conclusion is incorrect.

Andre wants to solve the equation . He uses a graphing calculator to graph and and finds that the graphs cross at the points and . Substitute each -value Andre found into the expression . Then evaluate the expression.

Why did neither solution make equal exactly 20?

Select all the solutions to the equation .

Here are two graphs that correspond to two patients, A and B. Each graph shows the amount of insulin, in micrograms (mcg) in a patient' body hours after receiving an injection. The amount of insulin in each patient decreases exponentially. Select all statements that are true about the insulin level of the two patients.

Han says this pattern of dots can be represented by a quadratic relationship because the dots are arranged in a rectangle in each step. Do you agree? Explain your reasoning.