Question

Write a polynomial function, f(x), such that f(x) is a second-degree function with zeros at x=2 and x=-3 such that f(7)=-6

Answer 1

To write a polynomial function f(x) that is second-degree and has zeros at x=2 and x=-3 and f(7)=-6, use the factored form of the quadratic equation. The function is f(x) = (-3/25)(x-2)(x+3)

Step-by-step explanation:

To write a polynomial function in standard form given the zeros and a point, we can use the factored form of the quadratic equation. The zeros are x=2 and x=-3, so the factors of the quadratic function are (x-2) and (x+3). To find the value of the leading coefficient, we can use the point (7,-6) by substituting the values into the function and solving for the coefficient.

f(x) = a(x-2)(x+3)

-6 = a(7-2)(7+3)

-6 = a(5)(10)

-6 = 50a

a = -6/50 = -3/25

Therefore, the polynomial function is f(x) = (-3/25)(x-2)(x+3)