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

In Exercises 49–52, write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 2x^2 but with the given point as the vertex. (5, 3)

Several graphs of the quadratic function ƒ(x) = ax^2 + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F. (Hint: Use the discriminant.) A > 0; b^2 - 4ac > 0

In Exercises 49–52, write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 2x^2 but with the given point as the vertex. (−10, −5)

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

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 sum is 16, find a pair whose product is as large as possible. What is the maximum product?

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