Height of a Projectile. A stone is thrown directly upward from a height of 30 ft with an

In Exercises 1 and 2, use the given graph to find (a) the vertex; (b) the axis of symmetry; and (c) the maximum or minimum value of the function.

In Exercises 1 and 2, use the given graph to find (a) the vertex; (b) the axis of symmetry; and (c) the maximum or minimum value of the function.

In Exercises 316, (a) find the vertex; (b) find the axis of symmetry; (c) determine whether there is a maximum or minimum value and find that value; and (d) graph the function.f 1x2 = x2 - 8x + 12

In Exercises 316, (a) find the vertex; (b) find the axis of symmetry; (c) determine whether there is a maximum or minimum value and find that value; and (d) graph the function.g1x2 = x2 + 7x - 8

In Exercises 316, (a) find the vertex; (b) find the axis of symmetry; (c) determine whether there is a maximum or minimum value and find that value; and (d) graph the function.f 1x2 = x2 - 7x + 12

In Exercises 316, (a) find the vertex; (b) find the axis of symmetry; (c) determine whether there is a maximum or minimum value and find that value; and (d) graph the function.g1x2 = x2 - 5x + 6

In Exercises 316, (a) find the vertex; (b) find the axis of symmetry; (c) determine whether there is a maximum or minimum value and find that value; and (d) graph the function.f 1x2 = x2 + 4x + 5

In Exercises 316, (a) find the vertex; (b) find the axis of symmetry; (c) determine whether there is a maximum or minimum value and find that value; and (d) graph the function.f 1x2 = x2 + 2x + 6

In Exercises 316, (a) find the vertex; (b) find the axis of symmetry; (c) determine whether there is a maximum or minimum value and find that value; and (d) graph the function.g1x2 = x2 2 + 4x + 6

In Exercises 316, (a) find the vertex; (b) find the axis of symmetry; (c) determine whether there is a maximum or minimum value and find that value; and (d) graph the function.g1x2 = x2 3 - 2x + 1

In Exercises 316, (a) find the vertex; (b) find the axis of symmetry; (c) determine whether there is a maximum or minimum value and find that value; and (d) graph the function.g1x2 = 2x2 + 6x + 8

In Exercises 316, (a) find the vertex; (b) find the axis of symmetry; (c) determine whether there is a maximum or minimum value and find that value; and (d) graph the function.f 1x2 = 2x2 - 10x + 14

In Exercises 316, (a) find the vertex; (b) find the axis of symmetry; (c) determine whether there is a maximum or minimum value and find that value; and (d) graph the function.f 1x2 = -x2 - 6x + 3

In Exercises 316, (a) find the vertex; (b) find the axis of symmetry; (c) determine whether there is a maximum or minimum value and find that value; and (d) graph the function.f 1x2 = -x2 - 8x + 5

In Exercises 316, (a) find the vertex; (b) find the axis of symmetry; (c) determine whether there is a maximum or minimum value and find that value; and (d) graph the function. g1x2 = -2x2 + 2x + 1

In Exercises 316, (a) find the vertex; (b) find the axis of symmetry; (c) determine whether there is a maximum or minimum value and find that value; and (d) graph the function.f 1x2 = -3x2 - 3x + 1

In Exercises 1724, match the equation with one of the graphs (a)(h), which follow.y = 1x + 322

In Exercises 1724, match the equation with one of the graphs (a)(h), which follow.y = -1x - 422 + 3

In Exercises 1724, match the equation with one of the graphs (a)(h), which follow.y = 21x - 422 - 1

In Exercises 1724, match the equation with one of the graphs (a)(h), which follow.y = x2 - 3

In Exercises 1724, match the equation with one of the graphs (a)(h), which follow.y = - 1 2 1x + 322 + 4

In Exercises 1724, match the equation with one of the graphs (a)(h), which follow.y = 1x - 322

In Exercises 1724, match the equation with one of the graphs (a)(h), which follow.y = -1x + 322 + 4

In Exercises 1724, match the equation with one of the graphs (a)(h), which follow.y = 21x - 122 - 4

Determine whether the statement is true or false.The function f 1x2 = -3x2 + 2x + 5 has a maximum value.

Determine whether the statement is true or false.The vertex of the graph of f 1x2 = ax2 + bx + c is - b 2a .

Determine whether the statement is true or false.The graph of h1x2 = 1x + 222 can be obtained by translating the graph of h1x2 = x2 right 2 units.

Determine whether the statement is true or false.The vertex of the graph of the function g1x2 = 21x - 422 - 1 is 1-4, -12.

Determine whether the statement is true or false.The axis of symmetry of the function f 1x2 = -1x + 222 - 4 is x = -2.

Determine whether the statement is true or false.The minimum value of the function f 1x2 = 31x - 122 + 5 is 5.

In Exercises 3140: a) Find the vertex. b) Determine whether there is a maximum or minimum value and find that value. c) Find the range. d) Find the intervals on which the function is increasing and the intervals on which the function is decreasing f 1x2 = x2 - 6x + 5

In Exercises 3140: a) Find the vertex. b) Determine whether there is a maximum or minimum value and find that value. c) Find the range. d) Find the intervals on which the function is increasing and the intervals on which the function is decreasingf 1x2 = x2 + 4x - 5

In Exercises 3140: a) Find the vertex. b) Determine whether there is a maximum or minimum value and find that value. c) Find the range. d) Find the intervals on which the function is increasing and the intervals on which the function is decreasingf 1x2 = 2x2 + 4x - 16

In Exercises 3140: a) Find the vertex. b) Determine whether there is a maximum or minimum value and find that value. c) Find the range. d) Find the intervals on which the function is increasing and the intervals on which the function is decreasingf 1x2 = 1 2 x2 - 3x + 5 2

In Exercises 3140: a) Find the vertex. b) Determine whether there is a maximum or minimum value and find that value. c) Find the range. d) Find the intervals on which the function is increasing and the intervals on which the function is decreasingf 1x2 = -1 2 x2 + 5x - 8

In Exercises 3140: a) Find the vertex. b) Determine whether there is a maximum or minimum value and find that value. c) Find the range. d) Find the intervals on which the function is increasing and the intervals on which the function is decreasingf 1x2 = -2x2 - 24x - 64

In Exercises 3140: a) Find the vertex. b) Determine whether there is a maximum or minimum value and find that value. c) Find the range. d) Find the intervals on which the function is increasing and the intervals on which the function is decreasingf 1x2 = 3x2 + 6x + 5

In Exercises 3140: a) Find the vertex. b) Determine whether there is a maximum or minimum value and find that value. c) Find the range. d) Find the intervals on which the function is increasing and the intervals on which the function is decreasingf 1x2 = -3x2 + 24x - 49

In Exercises 3140: a) Find the vertex. b) Determine whether there is a maximum or minimum value and find that value. c) Find the range. d) Find the intervals on which the function is increasing and the intervals on which the function is decreasing g1x2 = -4x2 - 12x + 9

In Exercises 3140: a) Find the vertex. b) Determine whether there is a maximum or minimum value and find that value. c) Find the range. d) Find the intervals on which the function is increasing and the intervals on which the function is decreasingg1x2 = 2x2 - 6x + 5

Height of a Ball. A ball is thrown directly upward from a height of 6 ft with an initial velocity of 20 ft>sec. The function s1t2 = -16t 2 + 20t + 6 gives the height of the ball, in feet, t seconds after it has been thrown. Determine the time at which

Height of a Projectile. A stone is thrown directly upward from a height of 30 ft with an initial velocity of 60 ft>sec. The height of the stone, in feet, t seconds after it has been thrown is given by the function s1t2 = -16t 2 + 60t + 30. Determine the time at which the stone reaches its maximum height and find the maximum height.

Height of a Rocket. A model rocket is launched with an initial velocity of 120 ft>sec from a height of 80 ft. The height of the rocket, in feet, t seconds after it has been launched is given by the function s1t2 = -16t 2 + 120t + 80. Determine the time at which the rocket reaches its maximum height and find the maximum height.

Height of a Rocket. A model rocket is launched with an initial velocity of 150 ft>sec from a height of 40 ft. The function s1t2 = -16t 2 + 150t + 40 gives the height of the rocket, in feet, t seconds after it has been launched. Determine the time at which the rocket reaches its maximum height and find the maximum height.

Maximizing Volume. Mendoza Manufacturing plans to produce a one-compartment vertical file by bending the long side of a 10-in. by 18-in. sheet of plastic along two lines to form a ^-shape. How tall should the file be in order to maximize the volume that it can hold?

Maximizing Area. A fourth-grade class decides to enclose a rectangular garden, using the side of the school as one side of the rectangle. What is the maximum area that the class can enclose

Maximizing Area. The sum of the base and the height of a triangle is 20 cm. Find the dimensions for which the area is a maximum.

Maximizing Area. The sum of the base and the height of a parallelogram is 69 cm. Find the dimensions for which the area is a maximum

Minimizing Cost. Classic Furniture Concepts has determined that when x hundred wooden chairs are built, the average cost per chair is given by C1x2 = 0.1x2 - 0.7x + 1.625, where C1x2 is in hundreds of dollars. How many chairs should be built in order to minimize the average cost per chair?

R1x2 = 5x, C1x2 = 0.001x2 + 1.2x + 60

R1x2 = 50x - 0.5x2 , C1x2 = 10x + 3

R1x2 = 20x - 0.1x2 , C1x2 = 4x + 2

Maximizing Area. A rancher needs to enclose two adjacent rectangular corrals, one for cattle and one for sheep. If a river forms one side of the corrals and 240 yd of fencing is available, what is the largest total area that can be enclosed?

Norman Window. A Norman window is a rectangle with a semicircle on top. Sky Blue Windows is designing a Norman window that will require 24 ft of trim on the outer edges. What dimensions will allow the maximum amount of light to enter a house?

Finding the Height of an Elevator Shaft. Jenelle drops a screwdriver from the top of an elevator shaft. Exactly 5 sec later, she hears the sound of the screwdriver hitting the bottom of the shaft. How tall is the elevator shaft? (Hint: See Example 7.)

Finding the Height of a Cliff. A water balloon is dropped from a cliff. Exactly 3 sec later, the

For each function f, construct and simplify the difference quotient f 1x + h2 - f 1x2 hf 1x2 = 3x - 7

For each function f, construct and simplify the difference quotient f 1x + h2 - f 1x2 hf 1x2 = 2x2 - x + 4

A graph of y = f 1x2 follows. No formula is given for f. Make a hand-drawn graph of each of the following. 4 2 4 4 2 (3, 2) (3, 2) (5, 0) x y (0, 2)g1x2 = -2f 1x2

A graph of y = f 1x2 follows. No formula is given for f. Make a hand-drawn graph of each of the following. 4 2 4 4 2 (3, 2) (3, 2) (5, 0) x y (0, 2)g1x2 = f 12x2

Find c such that f 1x2 = -0.2x2 - 3x + c has a maximum value of -225

Find b such that f 1x2 = -4x2 + bx + 3 has a maximum value of 50.

Graph: f 1x2 = 1 x - 522 - 3.

Find a quadratic function with vertex 14, -52 and containing the point 1-3, 12.

Minimizing Area. A 24-in. piece of string is cut into two pieces. One piece is used to form a circle while the other is used to form a square. How should the string be cut so that the sum of the areas is a minimum? 24 x 24 x