Answer:
vertex form: f (x) = 2 * (x - 2) ^ 2 - 8
factored form: f (x) = 2 * x * (x - 4)
Step-by-step explanation:
The first thing is to calculate the equation with its vertex form, we can calculate it knowing that it is formulated in the following:
f (x) = a * (x - h) ^ 2 + k
where
a is a coefficient
(h, k) is the vertex
Looking at the graph
The vertex is the point (2, -8), we replace and we are left with:
f (x) = a * (x - 2) ^ 2 - 8
Now, to calculate the value of the coefficient we are going to
mark a point on the graph
, we will select (0,0)
and replacing we have:
0 = a * (0 - 2) ^ 2 - 8
0 = 4 * a - 8
a = 8/4
a = 2
Therefore, we would be left with the equation of the function written in The first thing is to calculate the equation with its vertex form, we can calculate it knowing that it is formulated in the following:
f (x) = a * (x - h) ^ 2 + k
where
a is a coefficient
(h, k) is the vertex
Looking at the graph
The vertex is the point (2, -8), we replace and we are left with:
f (x) = a * (x - 2) ^ 2 - 8
Now, to calculate the value of the coefficient we are going to
mark a point on the graph
, we will select (0,0)
and replacing we have:
0 = a * (0 - 2) ^ 2 - 8
0 = 4 * a - 8
a = 8/4
a = 2
Therefore, we would be left with the equation of the function written in vertex form:
f (x) = 2 * (x - 2) ^ 2 - 8
Now for the factored form, we know it has the following structure:
f (x) = a * (x - x1) * (x - x2)
knowing that a is a coefficient
and that x1 and x2 are the zeros or x-intercepts of the function
Looking at the graph
The zeros or x-intercepts of the function are
x = 0 and x = 4
so
f (x) = a * (x - 0) * (x - 4)
f (x) = a * x * (x - 4)
To calculate the value of the coefficient a, we will take the point (2, -8), we replace:
-8 = a * 2 * (2 - 4)
-8 = 4 * a - 8 * a
4 * a = 8
a = 2
we replace and we have:
f (x) = 2 * x * (x - 4) and this would be the factored form of the equation
Now for the factored form, we know it has the following structure:
f (x) = a * (x - x1) * (x - x2)
knowing that a is a coefficient
and that x1 and x2 are the zeros or x-intercepts of the function
Looking at the graph
The zeros or x-intercepts of the function are
x = 0 and x = 4
so
f (x) = a * (x - 0) * (x - 4)
f (x) = a * x * (x - 4)
To calculate the value of the coefficient a, we will take the point (2, -8), we replace:
-8 = a * 2 * (2 - 4)
-8 = 4 * a - 8 * a
4 * a = 8
a = 2
we replace and we have:
f (x) = 2 * x * (x - 4) and this would be the factored form of the equation
