Question

which equation has a vertex of (-3, 4)?
y = 2(x + 3)^2+4
y = 2(x - 3)^2+4
y = 2(x - 3)^2-4
y = 2(x + 3)^2-4

Explanation:

Step1: Recall vertex - form of a quadratic function

The vertex - form of a quadratic function is $y = a(x - h)^2+k$, where $(h,k)$ is the vertex of the parabola.

Step2: Identify the values of $h$ and $k$ for each option

For a vertex of $(-3,4)$, we need $h=-3$ and $k = 4$ in the equation $y=a(x - h)^2+k$. When we substitute $h=-3$ into the formula, we get $y=a(x+3)^2 + 4$.

Answer:

The equation $y = 2(x + 3)^2+4$ has a vertex of $(-3,4)$.