Verified answer

y = x^2 + 18x + 80

y = x^2 + 18x + (18/2)^2 - (18/2)^2 + 80

y = (x + 9)^2 - 81 + 80

y = (x + 9)^2 - 1

if you are trying to find the vertex use the vertex equation. step 1. -18/2(1)= -9

step 2. take -9 and put back in to the equation x2+18x+80

Step 3 solve -9^2+18*-9+80=163 that is the vertex (-9,163)

x² + 18x + 80

Complete the square.

(x² + 18x) + 80

To complete the trinomial square,

halve the coefficient of x (18/2 = 9)

(trinomial square is (x+9)² )

and square the result (9² = 81)

(x² + 18x + 81) + 80

You are, in effect, adding 81 to the expression.

You have to then subtract 81 at the end.

(x² + 18x + 81) + 80 - 81

(If this had a number before the parentheses,

you would need to subtract the product of

that number and the number that completes

the trinomial square.)

(x + 9)² - 1

Complete the square.

(x2+18x+81)+80-81 u got the 81 from dividing the 18 by 2 and then squaring it and u need to subtract the 81 in the end to make it equal to ur orginal equation.

(x+9)^2 -1

Vertex: (-9,-1)

x2+18x+80

= (x^2 + 18x ) + 80

= (x^2 + 18x + 9^2) + 80 - 9^2 //// half of 18 is 9 ; add 9^2 & subtract 9^2 to keep eqn balanced

= (x+9)^2 - 1 //// factorise (x^2 +18x +81) to (x+9)^2 //80 -9^2 = 80 -81 = -1