Name:
Date: _______________
Algebra 1B
“Finding Zeros Graphically” page 1
Finding Zeros by Solving Equations Graphically
Here are the steps:
 Use algebra steps to rewrite the equation until it has 0 on one side.
 Graph the function that appears on the non-zero side (by hand or by calculator).
 Find the x-intercept (also called the zero) of the function. If you’re graphing by calculator, use the
zero command. (2nd Trace 2)
Example (by hand)
Solve the equation x + 3 = –3x + 7.

Steps to get 0 on one side:

Graph your result.

Where does the graph cross the x-axis?

Solution:
Example (by calculator)
Solve the equation x2 + 3 = –x + 9.

Steps to get 0 on one side:

Plug result into Y= screen then press zoom 6.

Use the 2nd Trace Zero command to find the zero.
“Left Bound?” – move cursor to the left of the
x-intercept then hit enter
“Right Bound?” – move cursor to the right of the
x-intercept then hit enter twice
Solution:
Algebra 1B
“Solving Equations Graphically” page 2
Practice (graphing by hand)
1. Solve these equations by doing algebra steps to get 0 on one side, making a single graph,
then finding the zero (the x-intercept of the graph).
a. x + 2 = –2x + 5
b.
1
2
x  4  3x  1
c. 4x – 3 = x + 3
Algebra 1B
“Solving Equations Graphically” page 3
2. Solve these equations by doing algebra steps to get 0 on one side, making a single graph on
the calculator, then finding the zero using the 2nd Trace Zero command.
a. x + 5 = 3x – 1
Solution: x =
b. 3x3 + 3 = –3x + 9
type x ^ 3 to get x3 on calculator
Solution: x =
c.
1
2
x  3  2x
Solution: x =
Algebra 1B
“Solving Equations Graphically” page 4
REVIEW: Solving by Graphing Both Sides
Directions for problems 3–6: Solve each equation two different ways: (a) using algebra steps,
(b) graphically. You should get the same answer from both methods. If not, try to find your mistake.
3. a. Solve 3x + 5 = –x – 3 using algebra steps.
b. Solve 3x + 5 = –x – 3 by graphing both sides.
c. What solutions did you get from the two methods?
Do the answers agree?
4. a. Solve –2x + 1 = 5 using algebra steps.
b. Solve –2x + 1 = 5 by graphing both sides.
c. What solutions did you get from the two methods?
Do the answers agree?
Algebra 1B
“Solving Equations Graphically” page 5
5. a. Solve
1
3
x  2 x  5 using algebra steps.
b. Solve
1
3
x  2 x  5 by graphing both sides.
c. What solutions did you get from the two methods?
Do the answers agree?
6. a. Solve
1
2
x+1=
1
2
x + 3 using algebra steps.
b. Solve
1
2
x+1=
1
2
x + 3 by graphing both sides.
c. What solutions did you get from the two methods?
Do the answers agree?
Algebra 1B
“Solving Equations Graphically” page 6
Directions for problems 7–12: Each problem asks you to solve an equation by two different
methods. You should get the same answer from both methods. If not, try to find your mistake.
7. a. Solve by graphing both sides on your calculator:
x3 – 2 = ½ x –
5
2

b. Solve by getting 0 on one side and graphing on your
calculator:
x3 – 2 = ½ x – 5 2

c. Compare parts a and b: did you get the same answer?
8. a. Solve algebraically: –4x – 2 = 6
b. Solve using graphs on your calculator: –4x – 2 = 6
c. Compare parts a and b: did you get the same answer?
Algebra 1B
“Solving Equations Graphically” page 7
9. a. Solve algebraically: 3(x – 1) = –x + 5
b. Solve using graphs on your calculator: 3(x – 1) = –x + 5
c. Compare parts a and b: did you get the same answer?
10. a. Solve by graphing both sides on your calculator:
x2 1 x  6
Your answer will be a decimal.
Round to three decimal places.

b.
Solve by getting 0 on one side and graphing on your
calculator: x 2  1  x  6 Your answer will be a decimal.
Round to three decimal places.

c. Compare parts a and b: did you get the same answer?
Algebra 1B
“Solving Equations Graphically” page 8