To convert the equation from standard form to vertex form, follow these steps:
1. Complete the square by adding and subtracting the square of half the coefficient of x in the equation.
y = x^2 + 6x - 9
First, take half of the coefficient of x (6/2 = 3) and square it (3^2 = 9). Add and subtract 9 within the parentheses:
y = x^2 + 6x + 9 - 9 - 9
2. Rearrange the equation by grouping the perfect square terms and the constant term separately:
y = (x^2 + 6x + 9) - 9 - 9
3. Simplify the grouped terms:
y = (x^2 + 6x + 9) - 18
4. Factor the perfect square trinomial within the parentheses:
y = (x + 3)(x + 3) - 18
5. Simplify further within the parentheses:
y = (x + 3)^2 - 18
Therefore, the equation y = x^2 + 6x - 9 is in vertex form: y = (x + 3)^2 - 18.
The vertex form of the equation is (x + 3)^2 - 18.
y=x^2+6x-9
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