More Chapter 10

1
More Chapter 10

• Solving Equations and Applications Using the
  Quadratic

2

• Read section 10.2, but skip Example 3.
• 10.2 1, 3, 9, 13, 17, 21, 23, 29
• Read pages 799-800 of section 10.7 on "Finding
  Intercepts".
• 10.7 31, 33, 37. Perform the following tasks
  Find the x-intercepts of the graph of the
  function, if any. Find the y-intercept. Find the
  vertex of the graph. Plot the vertex,
  x-intercepts, y-intercept, and the axis of
  symmetry. Plot a few additional points on the
  graph of the function and complete the sketch of
  the parabola.
• 10.7 41. Perform the following tasks Sketch the
  graph of f with a graphing calculator. Adjust the
  viewing window so that the x-intercepts and the
  vertex of the parabola are visible in your
  viewscreen. Use the MIN or MAX routine in the
  CALC menu to find the coordinates of the vertex.
  Label the vertex on your graph with these
  coordinates. Use the ZERO routine in the CALC
  menu to find the zeros (x-intercepts) of the
  given quadratic function. Label these points on
  your graph with their coordinates. Solve the
  equation f(x)0 using the quadratic formula.
  Place your solutions in simple radical form. Use
  a calculator to approximate each of the exact
  solutions found. Compare these solutions with
  those found in part (3).
• R.6 41. Use factoring to solve these equation.
• 6.3 49, 53, 61. Use factoring to solve these
  equations.
• Read examples 3 and 4 of section 10.3. Skip
  example 1 (we will discuss these "motion"
  problems later in chapter 7) and example 2.
• 10.3 33, 35, 37, 39. The new application in this
  section is the "falling body" problem. As we saw
  in class, both the distance that an object falls
  and the height of the object are given by
  quadratic functions.
• 10.3 25
• Read section 10.8
• 10.8 3, 5, 7, 9, 13. Perform each of the
  following tasks for these problems Tell your
  reader what each variable represents. What is the
  unknown? Find a formula for the quantity that is
  to be maximized or minimized. Then use the
  constraints in the problem statement to rewrite
  this formula so that the quantity is written as a
  function of a single variable only. Use the
  vertex formula to find the x-coordinate of the
  vertex of the function. Substitute this into your
  function to find the maximum or minimum value of
  your function. Answer the original question in a
  sentence or two. Be sure that your answer makes
  sense (for example, an answer for length or area
  cannot be negative).
• 10.8 37. Perform each of the following tasks for
  this problem Plot the data on graph paper. Load
  the data into your calculator and use the
  quadratic regression routine to find the
  "parabola of best fit" requested in part (a).
  Note that the problem indicates that the variable
  x should represent "years after 1992", so your
  x-data should run between 0 to 10. Plot both the
  data and the parabola of best fit on your
  calculator. If you need to, refer to the
  quadratic regression instructions. Use the
  quadratic function that you found in part (a) to
  make the prediction asked for in part (b).

3
The Quadratic Formula

• Lets Derive it!

4
Use It to Solve
5

• Plot the following showing the x-intercepts,
  y-intercept, the vertex, the axis of symmetry,
  and at least 3 points.

6
Section 10.3

• Applications
• Take 1

7
Equation of Motion

• Recall
• Negative initial velocity means you are moving
  toward the Earth.

8

• Falling Distance An object is dropped from a
  balloon that is 500 meters above the ground.
  About how long does it take to hit the ground?
• The pilot of the balloon throws another object at
  an initial velocity of 30 m/s (again from 500 m).
  How long does it take to hit the ground?
• How far from the balloon will the object be in 5
  seconds?

9

• Hang Time The NBAs Vince Carter has a vertical
  leap of about 36 in. What is his hang time? Use
  the formula

10
Solve the following for t
11
Section 10.8

• Max and Min Problems

12
Recall the 5-Steps

• What is the Question
• Translate
• Solve
• Check
• State

13

• Solarium You are building a rectangular solarium
  onto your house and have materials enough for a
  perimeter of 720 ft. You only need to build 3
  sides since it will attach to the house. What
  should the dimensions be to maximize the area?

14

• Cheap Plastic Crap Wal-Mart plans to make a
  napkin holder for the holidays out of a 8-cm by
  14-cm sheet of plastic with a Jolly Saint Nick
  embossed on it by bending it in 2 places. How
  tall should the napkin holder be to maximize the
  volume?

15

• Regressing Again Look at page 812, problems
  17-25
• Alternate Fuel The number of hybrid cars in the
  US during the last couple of years is given by

Use the data to fit a Quadratic model. Use the
model to predict how many hybrids in 2004.
16

• Page 476 Diet and Health.
• Form groups of 3.
• Use graph paper to make 2 scatterplots one for
  life expectancy and one for infant mortality.
• Each member of the group does one of the three
  models linear, quadratic, or cubic for each
  scatterplot.
• Decide as a group which is the best-fit.
• Be sure every group member answers all of the
  questions, 1a-e, 2a-e. Write the responses on our
  graph paper.