Question

convert the equations below to standard form

1. f(x)=-3(x + 4)^2 + 2

Explanation:

Step1: Expand the squared term

We know that \((a + b)^2 = a^2 + 2ab + b^2\). Here \(a=x\) and \(b = 4\), so \((x + 4)^2=x^{2}+8x + 16\). Then the function \(f(x)=- 3(x^{2}+8x + 16)+2\)

Step2: Distribute the - 3

Multiply - 3 with each term inside the parentheses: \(-3\times x^{2}=-3x^{2}\), \(-3\times8x=-24x\), \(-3\times16 = - 48\). So \(f(x)=-3x^{2}-24x-48 + 2\)

Step3: Combine like terms

Combine the constant terms \(-48\) and \(2\): \(-48+2=-46\). So \(f(x)=-3x^{2}-24x - 46\)

Answer:

\(f(x)=-3x^{2}-24x - 46\)