Question

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 + .

Answer 1

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)