Question

A parabola has roots 1+-\sqrt{5}. The y-intercept is the same as the equation 2x^2+3x+4. Write an equation for the parabola in factored form.

I had this as a thinking question in a test. I solved 1+-\sqrt{5} to get two roots and then figured 4 to be the y-int and 2 to be 'a' as the 'a' and 'c' values do not change. Am I correct?

Answer 1

if the roots are 1±√5, then
y = a(x-(1+√5))(x-(1-√5)) = a(x^2-2x-4)
The y-intercept is -4a, so you want -4a = 4 and a = -1
y = -(x-(1+√5))(x-(1-√5))