write a quadratic function f(x) = (x-8) (x+2) into vertex form

Answer:[ f(x) = (x - 3)^2 - 25 ]Step-by-step explanation:To convert the quadratic function ( f(x) = (x - 8)(x + 2) ) into vertex form, we need to follow these steps:Expand the quadratic function: [ f(x) = (x - 8)(x + 2) = x^2 + 2x - 8x - 16 = x^2 - 6x - 16 ]Complete the square: [ f(x) = x^2 - 6x - 16 ] To complete the square, we take the coefficient of ( x ), which is (-6), divide it by 2, and square it: [ \left(\frac{-6}{2}\right)^2 = 9 ] Add and subtract 9 inside the equation: [ f(x) = x^2 - 6x + 9 - 9 - 16 = (x - 3)^2 - 25 ]So, the vertex form of the quadratic function is: [ f(x) = (x - 3)^2 - 25 ]

Answered by johnpaulsayson660 | 2024-09-09