Modeling Quadratic Equations

The function below models the height h, in feet, of an object above the ground t seconds after being launched straight up in the air. What does the number 72 represent in the function?

• The maximum height, in feet, of the object

• The initial speed, in feet per second, of the object.

• The initial height, in feet, of the object.

• The maximum height, in feet, of the object.

If a is a solution of the equation below and a > 0, what is the value of a?

x² + 2x - 15 = 0

• 3

• 5

• 2

• -2

Tags

CCSS.HSA-REI.B.4B

The vertex of the parabola in the xy-plane below is (0, c). Which of the following is true about the parabola in the equation: y = -a(x - b)² + c?

• The vertex is (b, c) and the graph opens upwards.

• The vertex is (b, c) and the graph opens downward.

• The vertex is (-b, c) and the graph opens upwards.

• The vertex is (-b, c) and the graph opens downward.

The height, h, in feet of an object above the ground is given by h = -16t² + 32t + 240, t ≥ 0 where t is the time in seconds. Find the time it takes the object to strike the ground.

• 3

• 5

• 2

• 1

The height, h, in feet of an object above the ground is given by h = -16t² + 32t + 240, t ≥ 0 where t is the time in seconds. Find the time it takes the object to reach its maximum height.

• 5 seconds

• 3 seconds

• 2 seconds

• 1 second

The number of bacteria in a refrigerated food is given by f(x) = 25x² - 25x + 150 , for and where x is the temperature of the food in Celsius. At what temperature will the number of bacteria be minimal?

• 1

• -0.5

• 0.5

• -1

What is the y-intercept of?
y = ax² + bx + c 

• a

• b

• c

• y

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

Determine if the table is Linear, Quadratic or other.

• Linear

• Quadratic

• Other

Write the equation of the quadratic function that has a x-intercepts at 2 and 4 and passes through the point (3, 4).

• y = -4(x - 2)(x - 4)

• y = -4(x + 2)(x + 4)

• y = 4(x - 2)(x - 4)

• y = -0.25(x - 2)(x - 4)