$\"\"$

The form of quadratic function $\"\"$ .

The function $\"\"$ and its maximum value 48.

So $\"\"$ .

Since a < 0, the function has a maximum when $\"\"$ .

$\"\"$ (Substitute $\"\"$ )

The maximum value $\"\"$ . (Simplify)

The maximum value $\"\"$ . (Simplify) $\"\"$

The equation for the quadratic function that opens downward and contains x - intercepts are $\"\"$ is $\"\"$ .

$\"\"$ (Substitute a for $\"\"$ and b for 5)

$\"\"$ (Formula: $\"\"$ )

$\"\"$ (Simplify) $\"\"$

The equation for the quadratic function that opens upward is $\"\"$ and the equation for the quadratic function that opens downward is $\"\"$ .