Question

What is the vertex form for a vertex of (-3,-5) and when a= -2?

a) Oy=-2(x - 3)^2 + 5
b) Oy=-2(x + 3)^2 + 5
c) Oy=-2(x+3)^2 - 5
d) Oy= (x+3)^2-5

Answer 1

The vertex form of a quadratic equation with a vertex of (-3,-5) when a = -2 is Oy = -2(x + 3)^2 - 5.

Step-by-step explanation:

The vertex form of a quadratic equation where the vertex is (-3,-5) and the value of a is -2 can be expressed as Oy = -2(x + 3)^2 - 5. We start with the standard vertex form equation for a parabola which is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. In this case, since the vertex is (-3, -5), h is -3 and k is -5, and they are substituted into the equation resulting in y = -2(x - (-3))^2 - 5. We simplify this to Oy = -2(x + 3)^2 - 5, which matches option c).