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f(x) = (x + 6)(x - 4) Which of the fol...

`f(x) = (x + 6)(x - 4)`
Which of the following is an equivalent form of the function f above in which the minimum value of f appears as a constant or coefficient?

A

`f(x)=x^(2)-24`

B

`f(x)=x^(2)+2x-24`

C

`f(x)=(X-1)^(2)-21`

D

`f(x)=(x+1)^(2)-25`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to rewrite the function \( f(x) = (x + 6)(x - 4) \) in a form that highlights its minimum value. We will follow these steps: ### Step 1: Expand the function First, we will expand the function \( f(x) \). \[ f(x) = (x + 6)(x - 4) \] Using the distributive property (FOIL method): \[ f(x) = x^2 - 4x + 6x - 24 \] Combining like terms: \[ f(x) = x^2 + 2x - 24 \]
To solve the problem, we need to rewrite the function \( f(x) = (x + 6)(x - 4) \) in a form that highlights its minimum value. We will follow these steps: ### Step 1: Expand the function First, we will expand the function \( f(x) \). \[ f(x) = (x + 6)(x - 4) \] ...
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