Question

Put the equation y = x^2 + 26 x + 160 into the form y = ( x − h )^2 + k :

Answer 1

y = (x^2 + 26x) +160 complete the square

y = (x^2 + 26x ) + 160

Split our the constant and use the (b/2)^2

y = (x^2 + 26x + (26/2)^2 ) + 160 - (26/2)^2

since I am adding the new value I must subtract it from the end to keep the balance

y = (x^2 + 26x + 169) + 160 - 169

Now factor parenthesis and combine like terms

y = (x+13)^2 -9 its in the vertex form

Answer 2

`y = (x + 13)^2 - 9`

Explanation:

To write the given quadratic equation in the form y = ( x − h )^2 + k, we need to complete the square for the given equation.

y = x^2 + 26x + 160

Shift the constant to the left side of the equation:

y - 160 = x^2 + 26x

Divide the coefficient of x by 2 and add the square of the result to both sides of the equation:

26 / 2 = 13

So adding 13^2 to both sides of the equation to get:

y - 160 + (13)^2 = x^2 + 26x + (13)^2

y - 160 + 169 = (x + 13)^2

y + 9 = (x + 13)^2

y = (x + 13)^2 - 9