Write the equation of the quadratic function that has a vertex of (-5,9) and passes through the point (-7,-15) y=6(x+5)^2+9 y=6(x-5)^2+9 y=-6(x-5)^2+9 y=-6(x+5)^2+9

## Step 1The vertex form of a quadratic function is given by the equation:### \(y = a(x - h)^2 + k\)where \((h, k)\) is the vertex of the parabola.## Step 2In this problem, the vertex is given as \((-5, 9)\). Therefore, we can substitute and into the equation, which gives us:### \(y = a(x + 5)^2 + 9\)## Step 3We are also given a point \((-7, -15)\) that lies on the parabola. We can substitute and into the equation to solve for .## Step 4Substituting the values into the equation, we get:### \(-15 = a(-7 + 5)^2 + 9\)## Step 5Solving this equation for , we find that .## Step 6Substituting back into the equation, we get the final equation of the quadratic function:### \(y = -6(x + 5)^2 + 9\)