Finish the steps below to write a quadratic function for the parabola shown. use the vertex form, f(x) = a(x – h)2 + k, and substitute in the values for h and k. f(x) = a(x – 5)2 + 3 use another point and substitute in values for x and f(x). solve for a. 5 = a(6 – 5)2 + 3 write the function, using the values for h, k, and a. the function is f(x) = (x – )2 + .

Here we want to write the quadratic function for the parabola shown in vertex form.

We will get the function: f(x) = 2*(x - 5)^2 + 3

So the general function of a parabola with vertex (h, k) and leading coefficient a is:

f(x) = a*(x - h)^2 + k

Here, we know the formula:

f(x) = a*(x - 5)^2 + 3

where:

h = 5k = 3

So the vertex is the point (5, 3), and we only must find the value of a to completely determine the parabola's function

We also know that:

f(6) = 5

So we can solve:

5 = a*(6 - 5)^2 + 3

5 = a*(1)^2 + 3

5 = a + 3

5 - 3 = a = 2

So we just found the value of a, replacing this on the parabola's function we get:

f(x) = 2*(x - 5)^2 + 3

If you want to learn more about parabolas, you can read:

link

We have

f(x) = a(x – h)² + k
 we know the vertex v(5,3)
substitute in the values for h and k
f(x) = a(x – 5)² + 3 
Use another point and substitute in values for x and f(x). 
for the point (6,5)
Solve for a.
5 = a(6 – 5)2 + 3 > 5=a+3> a=2

The function is f(x)=a(x – h)2 + k > 2(x – 5)² + 3
f(x)= 2(x – 5)² + 3 > 2[x²-10x+25]+3=2x²-20x+50+3=2x²-20x+53
f(x)=2x²-20x+53

the answer is f(x)= 2(x – 5)² + 3 > (f(x)=2x²-20x+53)

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