Question

f(x) = 8x² - 2x + 3

g(x) = 12x² + 4x - 3

what is h(x) = f(x) - g(x)?

○ h(x) = 20x² + 2x
○ h(x) = -4x² - 6x
○ h(x) = -4x² - 6x + 6
○ h(x) = -4x² + 2x

Explanation:

Step1: Substitute the functions

Substitute \( f(x) = 8x^2 - 2x + 3 \) and \( g(x) = 12x^2 + 4x - 3 \) into \( h(x)=f(x)-g(x) \), we get:
\( h(x)=(8x^2 - 2x + 3)-(12x^2 + 4x - 3) \)

Step2: Distribute the negative sign

Distribute the negative sign to each term in \( g(x) \):
\( h(x)=8x^2 - 2x + 3 - 12x^2 - 4x + 3 \)

Step3: Combine like terms

Combine the \( x^2 \) terms: \( 8x^2-12x^2=-4x^2 \)
Combine the \( x \) terms: \( -2x-4x=-6x \)
Combine the constant terms: \( 3 + 3 = 6 \)
So, \( h(x)=-4x^2-6x + 6 \)

Answer:

\( h(x) = -4x^2 - 6x + 6 \) (the third option)