Identify the turning point of the function [tex]f(x) = x^2 - 2x + 8[/tex] by writing its equation in vertex form.
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Answer (2)
f ( x ) = x 2 − 2 x + 8 T o co n v er t t h e s t an d a r d f or m y = a x 2 + b x + c o f a f u n c t i o n in t o v er t e x f or m y = a ( x − h ) 2 + k Here t h e p o in t ( h , k ) i s c a ll e d a s v er t e x h = 2 a − b , k = c − 4 a b 2 a = 1 , b = − 2 , c = 8
h = 2 a − b = 2 − ( − 2 ) = 2 2 = 1 k = c − 4 a b 2 = 8 − 4 ( − 2 ) 2 = 8 − 1 = 7 y = ( x − 1 ) 2 + 7 S o t h e t u r nin g p o in t i s ( 1 , 7 )
The turning point of the function f ( x ) = x 2 − 2 x + 8 is found to be at ( 1 , 7 ) by converting it to vertex form. This was achieved by calculating the vertex using the formulas for h and k . The function in vertex form is f ( x ) = ( x − 1 ) 2 + 7 .
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