Among all pairs of numbers whose sum is 16, find a pair whose product is as large as possible. What is the maximum product?

Connecting Graphs with Equations Find a quadratic function f having the graphshown. (Hint: See the Note following Example 3.)

In Exercises 53–56, write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 3x^2 or g(x) = -3x^2, but with the given maximum or minimum. Maximum = 4 at x = -2

Connecting Graphs with Equations Find a quadratic function f having the graphshown. (Hint: See the Note following Example 3.)

In Exercises 53–56, write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 3x^2 or g(x) = -3x^2, but with the given maximum or minimum. Minimum = 0 at x = 11

Among all pairs of numbers whose difference is 24, find a pair whose product is as small as possible. What is the minimum product?

Height of an Object If an object is projected upward from an initial height of 100 ft with an initial velocity of 64 ft per sec, then its height in feet after t seconds is given by s(t) = -16t^2 + 64t + 100. Find the number of seconds it will take the object to reach its maximum height. What is this maximum height?

Find a value of c so that y = x^2 - 10x + c has exactly one x-intercept.

For what values of a does y = ax^2 - 8x + 4 have no x-intercepts?