Interpret Quadratic Functions

Lily wants to know how long her toy rocket will be in the air after she lights the fuse to launch it from a 1.5-foot launch pad.

Which one are we looking for?

• x at vertex

• y at vertex

• positive zero

Answer explanation

We are looking for how long the rocket is in the air, which corresponds to the positive zero of the function representing its height. Thus, the correct choice is 'positive zero'.

Using the graph of the quadratic function, identify the vertex.

• (4, -6)

• (0, 2)

• (.5, 0)

• (7.5, 0)

Answer explanation

The vertex of a quadratic function is the point where the graph changes direction. In this case, the vertex is at (4, -6), which is the lowest point on the graph, confirming it as the correct choice.

What is the minimum of this graph?

• (-2,6)

• (-0.5,-3.5)

• (-1,-3)

• (3,0)

Answer explanation

The minimum of the graph occurs at the point (-0.5,-3.5), where the y-value is the lowest compared to the other options. This indicates that (-0.5,-3.5) is the correct answer.

What are the zeros of the function? Choose all that apply.

• x = 0

• x = -3

• x = -6

• y = 18

Answer explanation

The zeros of a function are the values of x that make the function equal to zero. Here, x = 0 and x = -6 are correct because they satisfy this condition, while x = -3 and y = 18 do not.

A ball is thrown into the air with a speed of 32 feet per second. The function $ h = 32t - 16t^2 $ models the height of the ball after t seconds. How many seconds does it take for the ball to reach its maximum height?

• 0.75 seconds

• 1 second

• 2 seconds

• 4 seconds

Answer explanation

To find the maximum height, we use the vertex formula for a quadratic function. The time at maximum height is given by t = -b/(2a). Here, a = -16 and b = 32, so t = 32/(2*16) = 1 second. Thus, the ball reaches its maximum height at 1 second.

The graph shows the relationship between the height of a ball, y, thrown into the air and time, x. Which statement best describes the height of the ball?

• The maximum height is 2 meters.

• The maximum height is 4 meters.

• The height is increasing for 2 seconds.

• The height is increasing for 4 seconds.

Answer explanation

The graph indicates that the ball reaches a maximum height of 4 meters, as shown by the peak of the curve. The other options regarding the height increase are not relevant to the maximum height.

• A
• B
• C
• D

Which of the following represents a parabola that opens downwards?

What is the y-intercept of this parabola?

• (−1, 3)

• (−3, 11)

• (−2, 5)

• (0, 5)

What is the vertex of the given parabola?

• (1, 2)

• x = 2

• (2, 1)

• (0, -4)