GRAPHING QUADRATICS WITH THE CALCULATOR

GRAPHING:[Y= ] put in the equation, [ZOOM], [6(ZStandard)]

If the graph is not shown, then the CHANGE WINDOW to SEE GRAPH:

Make sure xmin < xmax and ymin < ymax

[WINDOW] and adjust YMAX (see farther up)

XMIN (see more left)XMAX (see more right)

YMIN (see farther down)

MAXIMUM: [2nd], [TRACE], [4 (maximum)]
Left Bound: move to the left of the maximum ( hill) [ENTER]

Right Bound: move to the right of the maximum (hill) [ENTER]

Guess: move to the maximum (hill) [ENTER]

MINIMUM: [2nd], [TRACE],[ 3 (minimum)]
Left Bound: move to the left of the minimum ( valley) [ENTER]

Right Bound: move to the right of the minimum ( valley) [ENTER]

Guess: move to the minimum ( valley) [ENTER]

ROOTS/ ZEROS/ X-INTERCEPTS:

[Y =] Y2 = 0, [GRAPH], [2nd], [TRACE], [5(intersect)]

Move cursor to intersection [ENTER], [ENTER], [ENTER]

To find when Y = #: [Y =] Y2 = #, [GRAPH], [2nd],[TRACE], [5(intersect)]
Make sure that your window shows the intersection

Move cursor to intersection ENTER, ENTER, ENTER

To find when X = #:

Option #1: [2nd], [TRACE], [1] (value), X= #, [ENTER]

Option #2: [2nd], [WINDOW] let TblStart = #, [2nd], [Graph]

Option #3: Substitute number into your equation and solve for y

To find INITIAL VALUE, look when x = 0.

Algebra 2: Unit 3Name ______

Quadratic Word Problems: Calculator Active

  • Set Up a quadratic function in standard , factored, or quadratic form.
  • Use your calculator commands to [GRAPH] and find points that would be helpful to answer the word problems.
  1. The area of a rectangle is 70 square centimeters. If the length is 4 cm longer than twice the width, find the dimensions of the length and width of the rectangle.
  1. The area of a rectangle is 54 square centimeters. If the length is 3 cm longer than twice the width, find the dimensions of the length and the width of the rectangle.
  1. The area of a triangle is 56 square inches. If the base is 2 inches shorter than twice the height, find the dimensions of the base and the height of the triangle.
  1. The area of a triangle is 32.5 square inches. If the base is 3 inches longer than twice the height, find the dimensions of the base and the height of the triangle.
  1. A frame of uniform width is placed around of a 5 x 8 photograph. If the area of the frame is 68 square inches, what is the uniform width of the frame?
  1. A frame of uniform width is placed around a 10 x 12 photograph. If the area of the frame is 135 square inches, what is the uniform width of the frame?
  2. A sidewalk of uniform width is placed around a 35 x 45 foot rectangular garden. If the area of the sidewalk is 2000 square feet, what is the uniform width of the sidewalk?
  1. A sidewalk of uniform width is placed around a 37 x 57 foot rectangular garden. If the area of the sidewalk is 1512 square feet, what is the uniform width of the sidewalk?
  1. A rocket is launched off a 100 foot building with an upward velocity of 80 feet per second. The flight of the rocket can be modeled by the equation: .
  2. What is the maximum height?
  1. When will it hit the ground?
  1. When will the rocket be at 130 feet?
  1. A rocket is launched off a 200 foot building with an upward velocity of 100 feet per second.
  2. Write an equation to model the flight of the rocket in the form:
  3. What is the maximum height?
  1. When will the rocket hit the ground?
  1. When will it be at 400 feet?
  1. Jim plans to put a fence in his backyard using his house at the fourth side. If he has a total of 400 feet of fencing materials, what is the maximum area that he can enclose? What are the dimensions of the maximized area?
  1. Jenny plans to put a fence in her backyard using her house at the fourth side. If she has a total of 800 feet of fencing materials, what is the maximum area that she can enclose? What are the dimensions of the maximized area?
  1. Eric is at the top of a cliff that is 500ft from the ocean’s surface. He is waiting for his friend to climb up and meet him. As he is waiting, he decides to start casually tossing pebbles off the side of the cliff. The equation that represents the height of his pebble tosses is s = -16t2 + 5t + 500 where s is the distance in feet and t=time in seconds.
  1. How long does it take the pebble to hit the water?
  2. If four seconds have gone by, what is the height of the pebble from the ocean?
  3. What is the highest point the pebble will go?
  1. The planning committee for a school play at North High School asked the business class to give them some estimates about income that could be expected at different price levels. The class did some market research to see what students would be willing to pay for tickets. They found the following model: I= -75p2 + 600pwhere I is income and p is Price of ticket.
  1. Find the predicted income if ticket prices are set at $7.
  2. What is the ticket price that will yield the maximum income?
  3. What is the maximum income?
  4. What ticket price will give an income of $1125?
  5. What is the most that they could charge before losing income?