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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 .
