Quadratic Feature from an Equation

Mathematical Equivalence

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A quadratic equation is shown below in factored form. Identify all the solutions of the equations.

y=(7x+2)(x-5)

The graph of a quadratic function is given. Which of the following statements are correct? Select all that apply

• The vertex is at (4,0)

• The y intercept is (0,3)

• The x-intercepts are (0,-3) and (0,1)

• The solutions to the equation of function are x=-3 and x=1

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The height of a water balloon that is launched into the air is given by h(t) = -5x²+20x+25. When will the balloon explode on the ground?

• 5 seconds

• 1 second

• 2 seconds

• 3 seconds

The height of a water balloon that is launched into the air is given by h(t) = -5t² + 40t + 2. From what height was the balloon released?

• 2 meters

• 5 meters

• 40 meters

• 20 meters

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation
h(t) = -16t² +128t  
When will the object reach its maximum height?

• 4 ft

• 0 seconds

• 0 ft

• 4 seconds

Rafael drops a ball from a third-story window. This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds.
h = -5t² + 45 
When is the ball at ground level?

• only at t = 0 seconds 

• only at t = 3 seconds

• only at t = 9 seconds

• at both t = 0 seconds and t = 3 seconds

Your nephew is standing on his deck, which is 4 feet off the ground. He tosses his toy up into the air. The equation h = -2t² + 7t + c models the toy's height, h, from the ground at t seconds after he threw it. How high is the toy after 1 second?

• 2

• 4

• 9

• 10

• 15