Question

write the quadratic function in standard form (y = ax^{2}+bx + c), given the function in vertex form (y=(x - 3)^{2}-4). a) (y=x^{2}-6x + 5) b) (y=x^{2}+5) c) (y=x^{2}-13) d) (y=x^{2}+6x + 5)

Explanation:

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

Use the formula \((a - b)^2=a^{2}-2ab + b^{2}\), where \(a = x\) and \(b = 3\). So \((x - 3)^2=x^{2}-6x + 9\). Then \(y=(x - 3)^2-4=x^{2}-6x + 9-4\).

Step2: Simplify the expression

Combine like - terms: \(y=x^{2}-6x+(9 - 4)=x^{2}-6x + 5\)

Answer:

A. \(y=x^{2}-6x + 5\)