Question

Write a quadratic fuction f whose zeros are -3 and -13

Answer 1

The zeros of a quadratic function are the points where the graph cuts the x axis.

If one zero is - 3, it means that

x = - 3

x + 3 = 0

Thus, one of the factors is (x + 3)

If another zero is - 13, it means that

x = - 13

x + 13 = 0

Thus, one of the factors is (x + 13)

Thus, the quadratic function would be

(x + 3)(x + 13)

We would open the brackets by multiplyingeach term inside one bracket by each term inside the other. Thus, we have

x * x + x * 13 + 3 * x + 3 * 13

x^2 + 13x + 3x + 39

x^2 + 16x + 39

Thus, the quadratic function is

f(x) = x^2 + 16x + 39