1. 10-3: Solving Quadratic Equations
Essential Questions:
How many solutions does a quadratic equation have?
How can you determine the number of solutions from the graph?

2. 10-3: Solving Quadratic Equations
The equation x2 + 3x – 4 = 0 is called a quadratic equation. It’s related to the quadratic function y = x2 + 3x – 4
The solutions of a quadratic equation and the x-intercepts of the quadratic function are the same
A quadratic equation can have one, two, or no real-number solutions. The solutions of a quadratic equation and the x-intercepts are often called the roots of the equation or zeros of the function.

3. 10-3: Solving Quadratic Equations
Example 1a: Solving by Graphing (Two solutions)
Solve each equation by graphing the related function
x2 – 4 = 0
Graph y = x2 – 4
Solutions are where the graph crosses the x-axis.
There are two solutions here
x = 2 or x = -2, which can be written as x = ±2

4. 10-3: Solving Quadratic Equations
Example 1b: Solving by Graphing (1 solution)
Solve each equation by graphing the related function
x2 = 0
Graph y = x2
Solutions are where the graph crosses the x-axis.
There is one solution here
x = 0

5. 10-3: Solving Quadratic Equations
Example 1c: Solving by Graphing (0 solutions)
Solve each equation by graphing the related function
x2 + 4 = 0
Graph y = x2 + 4
Solutions are where the graph crosses the x-axis.
Since the graph never crosses the x-axis, there is no solution

6. 10-3: Solving Quadratic Equations
Solving Quadratic Equations Using Square Roots
We can solve equations in the form x2 = c by finding the square roots of each side.
Solve 2x2 – 98 = 0
2x2 – 98 = Add 98 to each side
2x2 = 98 ÷ ÷2 Divide each side by 2
x2 = 49
x = ± Take the square root of 49
x = ±7 Remember the ±

7. 10-3: Solving Quadratic Equations
Your Turn: Solve each equation
t2 – 25 = 0
t = ±5
3n = 12
n = 0
2g = 0
No solution

8. 10-3: Solving Quadratic Equations
Assignment
Worksheet #10-3
Problems 1 – 29, odds