This document discusses two additional methods for solving quadratic equations: the quadratic formula and graphing. The quadratic formula can be used to solve any quadratic equation in standard form (ax^2 + bx + c = 0) by inputting the a, b, and c coefficients. Graphing involves changing the equation to y= form, plotting it on a calculator to find the x-intercepts, which are the solutions. Both methods are demonstrated with examples.

1. 6.7 Other Methods for
Solving Quadratic
Equations

2. 2 More Methods
So far we can solve by:
◦ Factoring
◦ Taking square roots
But, these only work for some
equations!
Two more ways are:
◦ The Quadratic Formula
◦ Graphing

3. The Quadratic Formula
Works to solve ANY quadratic
equation!
Remember, standard form is:
ax2 + bx + c = 0
Quadratic Formula:
https://www.youtube.com/watch?v=YCuXiujC3KE

4. Example:
Solve for x:

5. Example:
Solve for x:

6. Example:
Solve for x:

7. You Try!
Solve for x:

8. Solving by Graphing
Remember: a function’s zeros
are its x-intercepts.
Zeros happen where y = 0.

9. Solving
To solve a quadratic equation in
standard form, we can:
1. Change from “= 0” to “y = ”
2. Graph function on calculator.
3. Find x-intercepts.
 Menu
 Trace
 Graph Trace

10. Example 1:
Solve by graphing. Round to
the nearest tenth.

11. Example 2:
Solve by graphing:

12. Example 3:
Solve by graphing:

13. How Many Solutions?
Two
Imaginary
Solutions
One Real
Solution
Two Real
Solutions

14. You Try!
Solve by graphing: