The function f(t) = 4t2 − 8t + 7 shows the height from the ground f(t), in meters, of a roller coaster car at different times t. Write f(t) in the vertex form a(x − h)2 + k, where a, h, and k are integers, and interpret the vertex of f(t).

Vertex form is f(t) = 4 +3 and vertex is (1, 3).

Step-by-step explanation:

It is given that f(t)= 4 -8 t+7

Let's use completing square method to rewrite it in vertex form.

Subtract both sides 7

f(t)-7 = 4 -8t

Factor the 4 on the right side.

f(t) -7 = 4( - 2 t)

Now, let's find the third term using formula

Where 'b' is coefficient of 't' term here.

So, b=-2

Find third term using the formula,

which is equal to 1.

So, add 1 within the parentheses. It is same as adding  4 because we have '4' outside the ( ). So, add 4 on the left side of the equation.

So, we get

f(t) -7 +4 = 4( -2 t +1)

We can factor the right side as,

f(t) -3 = 4

Add both sides 3.

f(t) = 4 +3

This is the vertex form.

So, vertex is (1, 3)

step-by-step explanation: given equation a = h(b 1+b 2)

also we are given values of a, h and b 1 as :

a = 16, h = 4, and b 1 = 3.

in order to solve it for b 2, we need to plug the given values of   a, h and b 1 .

therefore, plugging values of   a, h and b 1   in given equation, we get

16 = 4( 3 + b 2)

first dividing both sides by 4, we get

4 = 3 + b 2

subtracting 3 from both sides, we get

4 -3 = 3 -3 + b 2

1 = b 2.