Interpret Graphs of Quadratic Functions

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'.

Identify the vertex and whether the graph opens up or down.

• (5, 2); opens up

• (5, 2); opens down

• (-5, 2); opens up

• (-5, 2); opens down

Answer explanation

The vertex of the parabola is (-5, 2), indicating the highest point. Since the graph opens upwards, it confirms that the correct choice is (-5, 2); opens up.

Which of the following graphs appropriately marks the axis of symmetry?

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Tags

CCSS.HSF-IF.C.7A

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.

If each mark on the x-axis represents one second, when did the object reach the ground?

• 2.5 seconds

• 6 seconds

• 5.5 seconds

• 5 seconds

(a)  

• A

• B

• C

• D

If the graph represents the path of a golf ball after it is hit with x as seconds and y as height in feet, mark on the graph where the ball hits the ground.

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.

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'.