Pre-AP Algebra 1 Unit 3 ‒ Quadratic Functions Practice Test

Find the rate of change from the graph.

Find the rate of change:

Find solutions to x ² +x−6=0.

Solve for x. 3x ² +13x−4=−10+2x

Solve for x. 7x² −4x+13=0

Billy is several years older than Johnny. Billy is one less than twice as old as Johnny, and their ages multiplied together make ninety-one. When will Billy be 1.5 times Johnny’s age?

A farmer is building a fence around a field. He knows that the length of the field is 11 meters more than twice its width. If he knows that the area of the field is 30 square meters, what is the perimeter, in meters, of the field?

A construction worker tosses a brick from a tall building. The brick’s height (in meters above the ground) ttt seconds after being thrown is modeled by h(t)=-5t 2 +20t+105 Suppose we want to know the height of the brick above the ground at its highest point. How far above the ground was the brick?

Tom started an entertainment company. The net value of the company (in thousands of dollars) t months after its creation is modeled by v(t)=4t 2 -24t-28 Tom wants to know when his company will be at its lowest net value. How many months after its creation does the company reach its lowest net value?

We can think of g as a translated (shifted) version of f . Complete the description of the transformation.  Use nonnegative numbers.To get the function g, shift f _____________ by _____________ units.

The parabola y=x² is shifted up by 4 units. What is the equation of the new parabola ?

Function g can be thought of as a translated (shifted) version of f(x)=x²

What is the equation for g(x)?

The parabola y=x² is scaled vertically by a factor of 7. What is the equation of the new parabola?

What is the missing constant term in the perfect square that starts with x²+10x ?

Imani and Todd were trying to solve the equation: x ² +6 x +5=8 x
Imani said, “I can factor the left-hand side into the zero product property.” (x+ 1)(x +5) , so I’ll solve using
Todd said, “I can solve by completing the square. If I add 4 to each side, I can rewrite the equation as ( x+ 3 ) ² =12 .”
Whose solution strategy would work?

What is the minimum possible value of the expression ?  3 x²+6 x−10 .

Which of the following is the correct solution when x ²−10 x−11=0 is solved using the quadratic equation?

What is the vertex of the parabola y=2 ( x−3 )² + 4 ?

What causes the graph of y=x²  to open downward?