Jesse tossed a paint brush off her roof. The height of the brush (in meters above the ground)t seconds after Jesse
tossed it is modeled by
-5+56 + 10
Jesse wants to know when the brush will hit the ground.
1) Rewrite the function in a different form (factored
or vertex) where the answer appears as a number in
the equation.
h(t) =
2) How many seconds after being thrown does the
brush hit the ground?
seconds
PLEASE HELP ASAP

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

■■■■■■■■■■■■■■■■■■■■■■■■■■

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 .

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

1. 34

2. 268

3. x=14.4

step-by-step explanation: