If the zeros of a quadratic function (a.k.a.: a parabola) are x = -3 and x = 5, that means that the graph of the parabola has x-intercepts (crosses the x-axis) at x = -3 and x = 5.
Working backward, we can then say that if the equation of the quadratic function were in factored form, it would look like this:
y = (x + 3)(x - 5) *remember that the signs of the x-intercepts are switched in factored form!
In order to find the values of a, b, and c, we will need to first convert the quadratic function from factored form into standard form: ax2 + bx + c. We can do this easily by F.O.I.L.-ing:
y = (x + 3)(x - 5)
= x2 - 5x + 3x -15 Combining like terms, we get:
y = x2 - 2x - 15 Standard Form
We can now see that a = 1, b = -2, and c = - 15.
Finally, to find the value of a + b + c, we just add them: 1 + (-2) + (-15) = -16