Express in the form a(x+k)^2+c

Question

i) 9x^2 +x-5

Answer 1

The Equation is 9x²+x-5.

Let y = 9x² + x - 5

Subtract 5 from each side.

y - 5 = 9x² + x

Factor out the co-efficient of the squared term.

y - 5 = 9(x² + x/9)

To change the expression into a perfect square add (half the x coefficient)² to each side of the expression.

x  coefficient = 1/9 then (half the x coefficient)² is (1/18) ² = 1/324.

y - 5 = 9(x² + x/9 + 1/324 - 1/324)

y - 5 + 9*(1/324) = 9(x+1/18)²

y - 5 + 1/36 = 9(x+1/18)²

y- 5 + 1/36 = 9(x+1/18)²

y - 179/36 = 9(x+1/18)²

y = 9(x+1/18)² + 179/36

Therefore the Equation is 9x²+x-5 is expressed as y = 9(x+1/18)² + 179/36 where a=9, k = 1/18 and c = 179/36