Question

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.What is the vertex form of the equation?

y=-x^2 + 12x-4

Answer 1

To convert the quadratic equation y=-x² + 12x - 4 to vertex form, we complete the square to obtain the vertex form y = -(x - 6)² + 32, with the vertex at (6, 32).

Step-by-step explanation:

The vertex form of a quadratic equation is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola. To convert the given quadratic equation y=-x² + 12x - 4 to vertex form, we'll complete the square.

1. Factor out the coefficient of the x² term: y = -1*(x² - 12x) - 4.
2. Find the term to complete the square: (-12/2)² = 36.
3. Add and subtract the found term inside the parenthesis: y = -1*(x² - 12x + 36 - 36) - 4.
4. Rewrite the equation by grouping the perfect square trinomial and combining the constants: y = -1*(x - 6)² + 36 - 4.
5. Simplify the constants to find the vertex form: y = -1*(x - 6)² + 32.

The vertex form of the equation is y = -1*(x - 6)² + 32, where the vertex is (h, k) = (6, 32)).