Question

an engineer uses the equation below to model the height of a cannonball shot straight up from ground level. in the model the height y (in feet) is a function of x, the number of seconds after the cannonball is shot.
$y = -16x^2 + 64x$
complete the parts below.
(a) graph the parabola $y = -16x^2 + 64x$. to do so, plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. then click on the graph-a-function button.

Explanation:

Step1: Find vertex x-coordinate

For $y=ax^2+bx+c$, $x_v=\frac{-b}{2a}$. Here $a=-16$, $b=64$.
$x_v=\frac{-64}{2(-16)} = 2$

Step2: Find vertex y-coordinate

Substitute $x=2$ into the equation.
$y_v=-16(2)^2+64(2) = -64 + 128 = 64$
Vertex: $(2, 64)$

Step3: Find left points (x=0,1)

For $x=0$: $y=-16(0)^2+64(0)=0$ → $(0,0)$
For $x=1$: $y=-16(1)^2+64(1)=48$ → $(1,48)$

Step4: Find right points (x=3,4)

For $x=3$: $y=-16(3)^2+64(3)=-144+192=48$ → $(3,48)$
For $x=4$: $y=-16(4)^2+64(4)=-256+256=0$ → $(4,0)$

Answer:

Points to plot:

1. Vertex: $(2, 64)$
2. Left points: $(0, 0)$, $(1, 48)$
3. Right points: $(3, 48)$, $(4, 0)$

Connect these points to graph the parabola $y=-16x^2+64x$.