Question 10 (2 points) Which of the following quadratic equations in standard form for a function that has a vertex at (3,6) and also goes through the point (4,4) a f(x)=-2x^2-12x-24 b f(x)=-2x^2+12x-12 C f(x)=x^2+6x+3 d f(x)=2x^2-12x+24

## Step 1<br />The vertex form of a quadratic function is given by the formula:<br />### \(f(x) = a(x-h)^2 + k\)<br />where \((h, k)\) is the vertex of the parabola.<br /><br />## Step 2<br />Given the vertex \((3,6)\), we can substitute these values into the formula to get:<br />### \(f(x) = a(x-3)^2 + 6\)<br /><br />## Step 3<br />We also know that the function passes through the point \((4,4)\). Substituting these values into the equation, we get:<br />### \(4 = a(4-3)^2 + 6\)<br /><br />## Step 4<br />Solving the equation for \(a\), we find that \(a = -2\).<br /><br />## Step 5<br />Substituting \(a = -2\) back into the equation, we get:<br />### \(f(x) = -2(x-3)^2 + 6\)<br /><br />## Step 6<br />Expanding and simplifying this equation, we get:<br />### \(f(x) = -2x^2 + 12x - 12\)