Question

A parabola has zeros at (-4,0) and (12,0) and has a maximum height of 20. What is the value of a for this parabola?​

Answer 1

Since the parabola has zeros at (-4,0) and (12,0), it can be written in factored form as:

f(x) = a(x + 4)(x - 12)

To find the value of a, we need to use the fact that the parabola has a maximum height of 20. The vertex of the parabola is halfway between the zeros, so it is located at:

x = (-4 + 12)/2 = 4

To find the maximum height, we can evaluate the function at x = 4:

f(4) = a(4 + 4)(4 - 12) = -80a

We know that the maximum height is 20, so we can set -80a = 20 and solve for a:

-80a = 20

a = -20/80

a = -1/4

Therefore, the value of a for this parabola is -1/4. The equation of the parabola is:

f(x) = (-1/4)(x + 4)(x - 12)

Answer 2

The equation of a parabola with zeros at (-4,0) and (12,0) and a maximum height of 20 is given by y = a(x + 4)(x - 12). To find the value of a, we need to substitute x = 0, y = 20 into the equation. We get:

20 = a(0 + 4)(0 - 12)

= a(-12)

a = 20/12

Therefore, the value of a for this parabola is 20/12.