GRAPHS

1
GRAPHS

• Chapter 1

2
Solving Equations in One Variable Using a
Graphing Utility

• 1.3

3
Solving Equations in One Variable

• If an equation can be solved algebraically, then
  an exact solution is found. If not, then a
  graphing calculator is used to find an
  approximate solution to TWO DECIMAL PLACES.

4
Solve Using Zero

• Write in the form
• Expression 0
• Graph Y1 expression
• Use ZERO to determine each x-intercept.

5
Solve Using Intersect

• Graph Y1 expression on the left and
  Y2expression on the right.
• Use INTERSECT to determine the x-coordinate of
  each point of intersection.

6
Solve Using Intersect

• After graphing, press 2nd trace.
• Choose intersect (5).
• Move the cursor onto one of the graphs and press
  enter.
• Move the cursor onto the other graph and press
  enter.
• Move the cursor on the intersection and hit
  enter.
• Repeat for other intersections.

7
Example--Solving with Calculator

• 3(2-x)2x-1
• Put 3(2-x) in
• Y1 and 2x-1
• In y2 and get
• The graph on
• The right. Then
• find the intersection.

8
Example--Solving Algebraically

• 3(2-x)2x-1
• 6 3x 2x 1
• 7 5x
• X 7/5 1.4

9
Example--Solving with Calculator

• X3 2x2 -9x 18 0
• Put the equation in y1 and use the zero function
  to find the zeroes or values that make the
  equation true.
• X 3, -2, and -3

10
Example--Solving Algebraically

• X3 2x2 -9x 18 0
• Factor by grouping. Separate into 2 groups.
• (X3 2x2 ) (-9x 18) 0
• Take out a common factor of each.
• x2(X 2 ) - 9(x 2) 0
• Factor out the common factor.
• (x2)(x2 9) 0
• Set each factor to zero and solve.
• X2 0 or x -2
• x2 9 0 or (x3)(x-3) 0 or x -3 or 3
• X 3, -2, and -3