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