Question

polynomials operations - review for test#2 (adding, subtracting, multiplying) the function $f(x) = -2(x - 3)^2 - 4$ can be written in standard form as $f(x) = -2x^2 + kx - 22$, where $k$ represents a number. what is the value of $k$?

Explanation:

Step1: Expand \((x - 3)^2\)

Using the formula \((a - b)^2 = a^2 - 2ab + b^2\), where \(a = x\) and \(b = 3\), we get \((x - 3)^2 = x^2 - 6x + 9\).

Step2: Multiply by -2

Multiply \(-2\) with the expanded form: \(-2(x^2 - 6x + 9)=-2x^2 + 12x - 18\).

Step3: Subtract 4

Now subtract 4 from the above result: \(-2x^2 + 12x - 18 - 4=-2x^2 + 12x - 22\).

Step4: Compare coefficients

The standard form is \(f(x)=-2x^2 + kx - 22\), comparing with \(-2x^2 + 12x - 22\), we see that \(k = 12\).

Answer:

\(12\)