Determine equation

Question

determine the equation of a parabola, algebraically, in the form y=a(x-h)^2+k given that it has a max value at y=7 and x-intercepts at (-4,0) and (-10,0). You may use a sketch to help in your solution.

Answer 1

Its vertex is at (h,k)

 

k = 7 (given)

 

h has to be the midpoint between the zeros, so

 

h = (-4 - 10)/2 = -7

 

So far, we have

 

y = a(x + 7)² + 7

 

At x = -4, y is zero.  Use this to find a.

 

0 = a(-4 + 7)² + 7

 

9a = -7

 

a = -7/9

 

y = (-7/9)(x + 7)² + 7

 

Test the answer.