Interpret Quadratic

What are the x- intercepts, roots, zeros?

• x= 0 and x= -4

• x= 0 and x= 4

• y= 0

• x= 2

Tags

CCSS.HSF-IF.C.7A

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.

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.

Tags

CCSS.HSF-IF.C.7A

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.

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 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.

Tags

CCSS.HSF-IF.C.7A

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.

Tags

CCSS.HSA.APR.B.3

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.

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.