What is y=x^2+8x-1 in the general form?

Question

Doing Quadratics.. the problem is in standard form now but i need it in the general form

[f(x)=a(x-h)^2+k]

Please help!

Answer 1

The standard form of f(x) is y = x² + 8x - 1.

General form of f(x) is y = a(x - h)^2 + k.

y = x² + 8x - 1

Add 1 to each side.

y + 1 = x² + 8x

x² + 8x = y + 1.

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

 Here x coefficient = 8. so, (half the x coefficient)² = (8/2)²= 16.

Add 16 to each side.

x² + 8x + 16= y + 1 + 16

(x - (-4))² = y + 17

Subtract 17 to each side.

y = (x - (-4))² - 17.

Compare the above equation with the general form of f(x) is y = a(x - h)^2 + k,

a = 1, h = -4, and k = -17.