There is nothing in the statement of the problem that says the quadratic is monic (leading coefficient is 1). So the most we can conclude is that a + b + c = -16a. This follows from writing the function as f(x) = a(x+3)(x-5), expanding, and adding the coefficients.

Cristina B.

asked • 03/06/20# If the zeros of a quadratic function f are -3 and 5 what is the value of a+b+c

## 3 Answers By Expert Tutors

Amanda B. answered • 03/07/20

Expert Algebra 1 Tutor with 10+ Years of Teaching Experience

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: ax**^{2 }**+ bx + c**. We can do this easily by F.O.I.L.-ing:

**y = (x + 3)(x - 5)**

= x^{2} - 5x + 3x -15 Combining like terms, we get:

** y = x**^{2 }**- 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**

(x + 3)(x - 5)

a = 1

b = -2

c = -15

**-16**

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