Question

NEED ANSWER ASPA.... PLS HURRY

The height of the new bike tunnel, y, in feet, is given by the following equation, where x is the horizontal distance, in feet, from the center line of the opening of the tunnel.

Note that negative x-values indicate the distance to the left of the center line, and positive x-values indicate the distance to the right of the center line.
Plot the points on the graph where the height of the tunnel is a maximum and where the height of the tunnel is zero feet.

Answer 1

The vertex is 0,36 and the two other points are -6,0 and 6,0

Explaination: Got it right on a mastery test on Edmentum #PlatoLivesMatter

Answer 2

we have that

`y=- x^(2) +36`

we know that
Is the equation of a vertical parabola open down
so
the vertex is a maximum

step 1
convert the equation of the parabola in the vertex form

`y=- x^(2) +36 \\ y-36=- x^(2)`

the vertex (h,k) is the point (0,36)

Part a) The point on the graph where the height of the tunnel is a maximum is (0,36)

Part b) The points on the graph where the height of the tunnel is zero feet is when y=0
so
for y=0

`- x^(2) +36=0 \\ x^(2) =36 \\ x= (+/-) 6`

the points are (-6,0) and (6,0)

see the attached figure