Interpret Quadratic Graph

Does this graph have a maximum or minimum value?

• maximum

• minimum

• neither

• both

Answer explanation

The graph has a minimum value because it reaches a lowest point, indicating that the function does not go below this value. Therefore, the correct answer is 'minimum'.

Jack wants to know how high the soccer ball will get if he kicks it straight up in the air. Which one are we looking for?

• x at vertex

• y at vertex

• positive zero

Answer explanation

We are looking for how high the soccer ball will get, which corresponds to the maximum height in a projectile motion. This is represented by the y-coordinate at the vertex of the parabola, making 'y at vertex' the correct choice.

What piece of information does c identify in the following equation?
y=ax²+bx+c

• Zeroes

• Axis of Symmetry

• Direction

• y-intercept

Answer explanation

In the equation y=ax²+bx+c, the term c represents the y-intercept. This is the value of y when x is 0, indicating where the graph intersects the y-axis.

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.

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'.

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.

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.

How long did it take the rocket to reach its maximum height?

Answer explanation

The rocket reaches its maximum height at the peak of its flight. The time taken to reach this point is typically measured in seconds. In this case, the correct answer is 0 seconds, indicating an immediate ascent to maximum height.

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.

What is the vertex of the given parabola?

• (1, 2)

• x = 2

• (2, 1)

• (0, -4)