Which equation has a vertex of `(-4,5)`?

Question

a. y=\left(x-4\right)^{2}+5
b. y=\left(x+4\right)^{2}-5
c. y=\left(x+4\right)^{2}+5
d. y=\left(x-4\right)^{2}-5

Answer 1

To determine which equation has a vertex of \((-4, 5)\), we need to look at the general form of a parabola given by \(y = a(x - h)^2 + k\), where \((h, k)\) is the vertex.

1. Identify the vertex: We are looking for the equation with vertex \((-4, 5)\). This means \(h = -4\) and \(k = 5\).

2. Evaluate each option:

   • a. \(y = (x - 4)^2 + 5\)

     • Vertex: \((4, 5)\) (not \((-4, 5)\))

   • b. \(y = (x + 4)^2 - 5\)

     • Vertex: \((-4, -5)\) (not \((-4, 5)\))

   • c. \(y = (x + 4)^2 + 5\)

     • Vertex: \((-4, 5)\) (matches)

   • d. \(y = (x - 4)^2 - 5\)

     • Vertex: \((4, -5)\) (not \((-4, 5)\))

3. Conclusion: The equation that has a vertex of \((-4, 5)\) is c. \(y = (x + 4)^2 + 5\).