Question

the areas of two rectangles can be represented by the functions shown. which function represents the difference in the areas, $h(x) = f(x) - g(x)$? $f(x) = 5x^2 - 2x + 1$ $g(x) = x^2 + 2x - 10$ options: $h(x) = 4x^2 - 4x - 11$; $h(x) = -4x^2 + 4x + 11$; $h(x) = 4x^2 - 4x - 9$; $h(x) = 4x^2 - 4x + 11$

Explanation:

Step1: Substitute the functions

We know that \( h(x)=f(x)-g(x) \), \( f(x) = 5x^{2}-2x + 1 \) and \( g(x)=x^{2}+2x-10 \). So we substitute these into the formula:
\( h(x)=(5x^{2}-2x + 1)-(x^{2}+2x-10) \)

Step2: Distribute the negative sign

Distribute the negative sign to each term in \( g(x) \):
\( h(x)=5x^{2}-2x + 1 - x^{2}-2x + 10 \)

Step3: Combine like terms

Combine the \( x^{2} \) terms: \( 5x^{2}-x^{2}=4x^{2} \)
Combine the \( x \) terms: \( -2x-2x=-4x \)
Combine the constant terms: \( 1 + 10 = 11 \)
So \( h(x)=4x^{2}-4x + 11 \)

Answer:

\( h(x)=4x^{2}-4x + 11 \) (the option with this function, assuming the last option is \( h(x)=4x^{2}-4x + 11 \))