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