Quadratic Equations Review

A company that manufactures model cars uses the function shown to estimate the profits from selling a certain model car set.

$$P\left(x\right)=-x^2+40x-375$$

In this equation, x = the price in dollars of each model car set and P(x) = annual profit in thousands of dollars. Select TWO statements that are true according to the function.

Hint: Use the "Completing the Square" method to answer this question.

Jarrett wrote the equation $$-5x=-4x-8$$ .

What is the value of x in this equation?

Does the equation $$x^2-8x-36=12$$ have the same solutions as the equation $$\left(x-4\right)^2=64$$ ?

Hint: Use the strategy "Completing the Square" to answer this question.

Caleb is making a wooden deck around 3 sides of his pool. Caleb has enough wood to make 372 feet of deck. The equation can be used to find x, the width of the deck in feet.

$$4x^2+112x=372$$

Rewrite the equation so it is in the form $$\left(x+p\right)^2=q$$ , where p and q are whole numbers. Type your response in the box.

Which are equivalent expressions?

For each expression shown in the picture, choose the equivalent expression.

Which equation is best to use to determine the zeros of the graph of $$y=6x^2-13x+6$$ ?

Consider the equation $$5x^2-18x-21=0$$ .

The method of completing the square can be used to transform the equation shown above into which equation?

A softball's height in feet x seconds after being thrown is given by the expression below.

$$-16x^2+48x+56$$

Which statement is TRUE about the softball?

A football is punted into the air. It's height,h, in meters after t seconds is given by the equation $$h=-4.9t^2+24.5t+1$$ .

Which statement is true?

Consider the equation $$x^2+14x-51=0$$ . Which represents the same equation in a different form?