Question

Jesse tossed a paint brush off her roof. The height of the

Answer 1

Answer:

Below

Step-by-step explanation:

1):

-5t^2 + 5t +10 is a qudratic equation so the path created by the tossed paint brush will be a parabola.

● -5t^2 + 5t +10 has the form ax^2 +bx +c

● a = -5

● b = 5

● c = 10

The vertex of this parabola has the coirdinates(-b/2a ; f(-b/2a) )

● -b/2a = -5 / 2×(-5) = 5/10 = 1/2 = 0.5

● f(0.5) = -5×0.5^2 + 5×0.5 +10 = 11.25

So the vertix coordinates are:

● (0.5,11.25)

(Picture below)

The vertex form is:

● a (x-h)^2 + k

● (h,k) are the coordinates of the vertex

So the vertex form of this function is:

● -5(t-0.5)^2 +11.25

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2):

The path is a parabola.

Before the brush is thrown the height was 0 and when it hits the ground again it is 0 .

The height is 0 when t reaches the roots of this function.

You can graph the function and extract the roots without calculations.

(-1,0) and (2,0) are the roots.

● 2-(-1) = 2 +1 = 3

So the brush falls after 3 s .