Answer:
f(x)=(x-2)(x-4)
Step-by-step explanation:
A simplified quadratic gives us the x-intercepts or the roots of the equation. Here, the roots are factors set equal to zero, where (2-2) equals zero and (-4+4) equals zero.
Substituting -5 for f(x) and 1 for x should give you an equal answer.
Answer: f(x) = (x − 2)(x + 4)
Step-by-step explanation:
These quadratic functions are written in factored form. In this form. the roots, also called the solutions or zeros, are given to us in a way by use of the zero product property.
Next, we will review the given options. Only two of these have roots of -4 and 2 which helps us narrow down our answer options.
f(x) = (x − 2)(x + 4) ➜ x = 2, -4 ✓
f(x) = (x − 2)(x − 4) ➜ x = 2, 4 ✗
f(x) = 4(x − 2)(x + 4) ➜ x = 2, -4 ✓
f(x) = 4(x − 2)(x − 4) ➜ x = 2, 4 ✗
Next, we can confirm which is the answer by substituting 1 from the point (1, -5). We should get -5.
f(x) = (x − 2)(x + 4)
f(1) = (1 − 2)(1 + 4)
f(1) = (-1)(5)
f(1) = -5 ✓
f(x) = 4(x − 2)(x + 4)
f(1) = 4(1 − 2)(1 + 4)
f(1) = 4(-1)(5)
f(1) = -20 ✗
