Put the following functions into standard form by completing the square. Use proper notation throughout.

Question

f(x)=x²+2x-7

Answer 1

f(x) = x² + 2x - 7

 

Take half of 2, square it and add and subtract it

 

f(x) = x² + 2x + 1 - 1 - 7

 

f(x) + (x+1)² - 8

Answer 2

Add and subtract b²/(4a) = 2²/[4(1)] = 1

 

x² + 2x - 7 = x² + 2x - 7 + 1 - 1 = (x² + 2x + 1) + (-7 - 1) = (x + 1)² - 8

 

f(x) = (x + 1)² - 8

 

This is in the form

 

f(x) = a(x - h)² + k

 

a = 1

h = -1

k = -8