Question

Find the equation of a quadratic function with zeros at x = 2 and x = 4 and y-
intercept (0,8). Give your answer in standard form.

Answer 1

Answer:

Since we know the zeroes of the function we can write:

y = a(x - 2)(x - 4) but we need to solve for a. Thankfully, we know that (0, 8) belongs to the line so we can plug these values in for x and y to solve for a. We get:

8 = a(0 - 2)(0 - 4)

8 = a * (-2) * (-4)

8 = 8a

a = 1 so the equation is y = 1(x - 2)(x - 4) or just y = (x - 2)(x - 4) for short.

Turning this into standard form we get y = x² - 6x + 8.