Question

The vertex of the parabola below is at the point (1,5), and the point (2,8) ison the parabola. What is the equation of the parabola?A. y= 3(x+ 1)2 + 5B. y = 2(x + 1)2 + 5C. y= 2(x - 1)2 + 5D. Y = 3(x - 1)2 + 5

Answer 1

To find the equation of the parabola use the next equation

f(x) = ax² + bx +c

f(x) = a(x-h)² + k

when the vertex is (h,k) = (1,5) and (2,8)= (x,y), so:

f(x) = a(x-1)² + 5

8 = a(2-1)² + 5

8 = a(1)² + 5

8 = a + 5

solve for a

8-5 = a

3 = a

Now we know the value of a so replace on the equation f(x) = a(x-1)² + 5.

The answer would be y = 3(x-1)² + 5