Question

write the quadratic function in standard form. use a graphing calculator table or graph to verify your work
$f(x) = -3(x - 2)^2 - 2$
$f(x) = \square$

Explanation:

Step1: Expand \((x - 2)^2\)

We use the formula \((a - b)^2 = a^2 - 2ab + b^2\), where \(a = x\) and \(b = 2\). So \((x - 2)^2 = x^2 - 4x + 4\).

Step2: Multiply by -3

Now we multiply \(-3\) with the expanded form: \(-3(x^2 - 4x + 4)=-3x^2 + 12x - 12\).

Step3: Subtract 2

Subtract 2 from the above result: \(-3x^2 + 12x - 12 - 2=-3x^2 + 12x - 14\).

Answer:

\(f(x)=-3x^2 + 12x - 14\)