Question

Write a quadratic function in intercept form whose graph has given x- intercepts and passes through the given point.
x-intercepts: -2,2
Point: (-4,8)

Answer 1

Intercept form of quadratic function is:

f(x) = a(x - p)(x - q)

where p and q are the intercepts:

So we have:

f(x) = a(x - 2)(x + 2)

Now we just have to find the value of a. We can simply input the point (-4,8) to find a:

8 = a(-4 - 2)(-4 + 2)
8 = a(-6)(-2)
8 = 12a
8/12 = a
2/3 = a

Thus the quadratic function given point (-4,8) and intercepts 2 and -2 is
f(x) = 2/3(x - 2)(x + 2)