Question

The $x$-intercepts of the parabola $y = x^2 + bx + c$ are $(-3,0)$ and $(5,0). $ what is the equation of the parabola? enter your answer in the form $y = ax^2 + bx + c$.

Answer 1

y = x^2 - 2x - 15

Explanation:

Since the x-intercepts are (-3,0) and (5,0), the roots of the quadratic are -3 and 5. This means that the equation of the parabola is

y = (x + 3)(x - 5), which expands to y = x^2 - 2x - 15