Question
write the quadratic function f(x) = 2(x-4)^2 -8 in factored form
Answers
GPT 3.5
f(x) = 2(x-4)^2 - 8
First, expand the squared term:
f(x) = 2(x^2 - 8x + 16) - 8
f(x) = 2x^2 - 16x + 32 - 8
f(x) = 2x^2 - 16x + 24
Next, factor out a common factor of 2:
f(x) = 2(x^2 - 8x + 12)
Now, we need to find two numbers that multiply to 12 and add up to -8 (the coefficient of x):
-6 and -2 fit these criteria, so we can factor the quadratic as:
f(x) = 2(x - 6)(x - 2)
Therefore, the factored form of the quadratic function f(x) = 2(x-4)^2 - 8 is f(x) = 2(x - 6)(x - 2).
First, expand the squared term:
f(x) = 2(x^2 - 8x + 16) - 8
f(x) = 2x^2 - 16x + 32 - 8
f(x) = 2x^2 - 16x + 24
Next, factor out a common factor of 2:
f(x) = 2(x^2 - 8x + 12)
Now, we need to find two numbers that multiply to 12 and add up to -8 (the coefficient of x):
-6 and -2 fit these criteria, so we can factor the quadratic as:
f(x) = 2(x - 6)(x - 2)
Therefore, the factored form of the quadratic function f(x) = 2(x-4)^2 - 8 is f(x) = 2(x - 6)(x - 2).