Question

Rewrite the equation into vertex form.
m(x)=-x^2-8x-15

Answer 1

To rewrite the equation m(x) = -x^2 - 8x - 15 into vertex form, complete the square process is used, resulting in the vertex form m(x) = -(x + 4)^2 + 1, with the vertex at (-4, 1).

Step-by-step explanation:

To rewrite the quadratic equation m(x) = -x^2 - 8x - 15 into vertex form, we need to complete the square. Here are the steps to do so:

1. Start with the original equation: m(x) = -x^2 - 8x - 15.
2. Factor out the coefficient of the x^2 term, which is -1 in this case, from the x terms: m(x) = -1(x^2 + 8x) - 15.
3. Find the number to complete the square for the expression in the parenthesis. This number is ((8/2))^2 = 16.
4. Add and subtract this number inside the parenthesis, keeping the equation balanced: m(x) = -1(x^2 + 8x + 16 - 16) - 15.
5. Rewrite the perfect square trinomial and combine constants: m(x) = -1((x + 4)^2) - 15 + 16.
6. Simplify the equation to vertex form: m(x) = -(x + 4)^2 + 1.

The vertex form of the equation m(x) is now m(x) = -(x + 4)^2 + 1, where the vertex of the parabola is at (-4, 1).