Question

question 22 (mandatory) (1 point)
which function represents $f(x) = -(x + 5)^2 - 4$ written in standard form?
\bigcirc a) $f(x) = -x^2 - 10x - 29$
\bigcirc b) $f(x) = x^2 + 10x + 21$
\bigcirc c) $f(x) = -x^2 - 10x - 21$
\bigcirc d) $f(x) = -x^2 + 10x + 21$

Explanation:

Step1: Expand the square term

First, expand \((x + 5)^2\) using the formula \((a + b)^2 = a^2 + 2ab + b^2\). Here, \(a = x\) and \(b = 5\), so \((x + 5)^2 = x^2 + 10x + 25\).

Step2: Apply the negative sign

Now, multiply the expanded term by \(-1\): \(-(x^2 + 10x + 25)= -x^2 - 10x - 25\).

Step3: Subtract 4

Next, subtract 4 from the above result: \(-x^2 - 10x - 25 - 4\).

Step4: Simplify the constant terms

Simplify \(-25 - 4\) to get \(-29\). So the function in standard form is \(f(x)= -x^2 - 10x - 29\).

Answer:

a) \(f(x) = -x^2 - 10x - 29\)