Solving Quadratic Equations by the Quadratic Formula

Lesson 9.5

Algebra 2

Solving a Quadratic Equation

02 caxcax 2

a

c

a

ax

2

a

cx

2

a

cx

2

a

cx

0,

a

cwhere

Given a quadratic equation, we have found the solutions by finding the square roots.

Given:

Solution:

Example: 2x2 - 4 = 0

Quadratic Formula

a

acbbx

2

42

040 2 acbandawhen

Given a quadratic equation in standard form:

02 cbxax

The solutions can be found by: Memorize

Important Note: The solutions (the values of x) are the roots or x-intercepts of the graph of the quadratic equation.

Using the Quadratic Formula

1. Rewrite the equation in standard form.

2. Identify the values of a, b, and c.

3. Substitute the values into the quadratic formula.

4. Simplify. You will obtain two solutions.

5. Check both solutions in the original equation.

Example #1

72

14

2

59

22

4

2

59

2

59

2

259

2

56819

)1(2

)14)(1(499

2

4

14,9,1

0149

149

22

2

2

a

acbbx

cba

xx

xxGiven:

a

acbbx

2

42

Example #2 a

acbbx

2

42

xx 2152 Given:

Solve using the quadratic formula.

Remember: The solutions (the values of x) are the roots or x-intercepts of the graph of the quadratic equation.

Number of solutions of a quadratic

The part of the quadratic formula under the radical sign (b2-4ac) is called the discriminant.

If b2-4ac is positive (>0), then the equation has two real solutions.

If b2-4ac is zero, then the equation has one solution. If b2-4ac is negative (<0), then the equation has no

real solutions (only imaginary).

Summary: Quadratic Formula

a

acbbx

2

42

040 2 acbandawhen

Given a quadratic equation in standard form:

02 cbxax

The solutions can be found by: Memorize

Important Note: The solutions (the values of x) are the roots or x-intercepts of the graph of the quadratic equation.

End of Lesson