Question

which quadratic function is the standard form of the equation shown?
$f(x) = x + 8 + 2x + 5x^2$
\bigcirc $f(x) = 8 + 5x^2 + 2x + x$
\bigcirc $f(x) = x + 2x + 5x^2 + 8$
\bigcirc $f(x) = 8 + 3x + 5x^2$
\bigcirc $f(x) = 5x^2 + 3x + 8$

Explanation:

Step1: Combine like terms for x

The original function is \( f(x) = x + 8 + 2x + 5x^2 \). Combine the \( x \) terms: \( x + 2x = 3x \).

Step2: Rearrange in standard form

Standard form of a quadratic function is \( f(x)=ax^2 + bx + c \) (where \( a
eq0 \)) with descending powers of \( x \). So we rearrange the terms: \( f(x)=5x^2 + 3x + 8 \).

Answer:

\( f(x) = 5x^2 + 3x + 8 \) (the fourth option)