Solving Equations by Graphing - x-intercept Method

• Move all terms to the left hand side of the equation, so that zero is on the right hand side.

Example

Solve the equation:

1x3xx2

01x3xx2 • Let Y1 = left hand side of the equation.

Slide 2

• Find a suitable graph window that shows where the graph intersects the x-axis. In this case ZOOM|ZStandard is sufficient.

Example

Solve the equation:

1x3xx2

01x3xx2

Solving Equations by Graphing - x-intercept Method

• We now want to find the x-intercepts. These are the points (x,0) where, for a given value of x, the y-value is zero, or Y1 = 0.

Slide 3

Example

Solve the equation:

1x3xx2

01x3xx2

• Use CALC|zero to find the x-intercepts (explained in another slideshow).

• The point on the left is approximately (- 0.24, 0).

• The point on the right is approximately (4.24, 0)

Solving Equations by Graphing - x-intercept Method

• Approximate solutions to the equation are x = - 0.24, 4.24.

Slide 4

• To confirm that these are correct solutions, use TABLE.

• TBLSET, Ask

• TABLE

• Enter the two x-values in the x-column and notice that the values in the Y1 column are approximately zero, as they should be.

01x3xx2

Solving Equations by Graphing - x-intercept Method

Slide 5

Solving Equations by Graphing - x-intercept Method

• The solutions just found were to the equation

Example

Solve the equation:

1x3xx2

01x3xx2

01x3xx2

• Note that these are the same x-values that satisfy the original equation

1x3xx2

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