Question

Convert f(x)=3x²+6x-9 to vertex form and identify the vertex

Answer 1

To convert the quadratic function f(x) = 3x² + 6x - 9 to vertex form, complete the square by dividing the coefficient of the x-term by 2 and squaring it. The vertex form is f(x) = 3(x + 1)² - 12, and the vertex is (-1,-12).

Step-by-step explanation:

To convert the quadratic function f(x) = 3x² + 6x - 9 to vertex form, we need to complete the square. The vertex form of a quadratic function is given by f(x) = a(x - h)² + k, where (h,k) represents the coordinates of the vertex. Here's how to do it:

1. Step 1: Divide the coefficient of the x-term by 2 and square it. In this case, it would be (6/2)² = 9.
2. Step 2: Add the result from Step 1 inside the parentheses, but also subtract it outside the parentheses to maintain the equivalence. This gives us f(x) = 3(x² + 2x + 1) - 9 - 3 = 3(x + 1)² - 12.

Therefore, the quadratic function f(x) = 3x² + 6x - 9 in vertex form is f(x) = 3(x + 1)² - 12. The vertex is (-1,-12).