Two numbers add up to 118, and when multiplied, give a product that is a maximum. Solve for this product.

Find out the equation of the parabola in the vertex form for the given condition:
(a) Shape of the parabola same as f(x) = -7x² 

(b) Maximum = -3 at x = 6

Find out the equation of the parabola in the vertex form for the given condition:
(a) Shape of the parabola same as f(x) = 13x² 

(b) vertex of the parabola (-1, -1)

Using the following description of the graph of a quadratic function, determine the domain and range. The vertex is (-5, -6) and the parabola opens up.

Find out whether the function has a minimum value or a maximum value without graphing it. Determine the minimum or maximum value and the point where it occurs. Also, find out the domain and range of the function. f(x) = 9x²-54x+83

For the given quadratic equation, write down the coordinates of the vertex of the parabola. f(x) = 7(x -5)² -3