Problems Solving with Quadratic Equations

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation

s(t) = –16t² + 64t + 80

What will be the object's maximum height?

• 2 ft

• 80 ft

• 144 ft

• 64 ft

Heather dropped a water balloon over the side of her school building from a height of 80 feet. The approximate height of the balloon at any point during its fall can be represented by the following quadratic equation: h = -16t^2 + 80 About how long did it take for the balloon to hit the ground?

• 1.73 seconds

• 2.24 seconds

• 2.45 seconds

• 2.83 seconds

What is the first step in solving the equation 3x^2+12x=9 by completing the square?

• Add 36 to each side of the equation.

• Factor the left side as 3x(x+4).

• Extract the square roots of both sides of the equation.

• Divide the whole equation by 3.

The following are the steps solving quadratic equations using quadratic formula.

I. Identify the values of a, b and c.

II. Rewrite the equation into standard form.

III. Perform the operations

IV. Substitute the values in the formula.

 Which of the following is the correct sequence?

• I, II, III, IV

• II, I, IV, III

• II, IV, I, III

• I, IV, II, III

The quadratic function y = -2x² + 4x + 6 is pictured. What are the solutions to the equation 7.5 = -2x² + 4x + 6?

• x = 0.5

• x = 1.5

• x = 1

• x = 8

• x = 6

Select the solutions to the equation

4x² + 11x + 7 = 0

• x = - 1.75

• x = 6

• x = - 1

• x = 1

What are the solutions for this quadratic equation?

• -4 and 0

• 4 and 0

• -2 and 4

• -2 and -4

What are the solutions to the quadratic equation?

• x = -4

• x = 1

• x = -1

• x = 2

• x = 4

You jump off a 24 foot high cliff and your fall is modeled by the function:

h(t) = -16t² + 8t + 24

How long would it take you to hit the water?

• 8 seconds

• 1 second

• 1.5 seconds

• 1/4 second

A diver is standing on a platform above the pool. He jumps form the platform with an initial upward velocity of 8 ft/s. Use the formula: h(t) = −16 t² + 8t + 24

How high is the platform?

• .25 ft

• 24 ft

• 25 ft

• 8 ft