Solve Quadratic Equations - Quadratic Formula

1
Unit 6 Solving Quadratic Equations

• Learning Goal
• I can solve a quadratic equation using the
  quadratic formula.

2
Derive(make) the Quadratic Formula by Completing
the Square

• Quadratic Formula

Divide by a so that x2 has a coefficient of 1.
Simplify.
Move the constant to the opposite side of the
equal sign.
Simplify.
Add half of b squared to both sides.
Factor the left side and simplify the exponential
expression. Rearrange the right side.
Find common denominator (4a2) so that we can
simplify the fraction.
Simplify the fraction.
3
Derive(make) the Quadratic Formula by Completing
the Square

• Quadratic Formula

This is copied from the previous page.
Take the square root of both sides.
Simplify the radical.
Take the square root of 4a2 which equals 2a.
Subtract b/2a from both sides.
Simplify the fraction.
This is the quadratic formula. Commit it to
memory.
4
Using the Quadratic Formula to Solve Quadratic
Equations

• Quadratic Formula

1
Set equation equal to zero. Done for us!!
Identify a, b, and c. (ax2 bx c 0 is
standard form.
a 1, b 6, c 2
Write the formula.
Substitute a, b, and c.
Simplify. (PEMDAS)
Simplify. (PEMDAS)
Take the square root.
Separate into two problems ( and -).
Simplify.
5
Using the Quadratic Formula to Solve Quadratic
Equations

• Quadratic Formula

Set equation equal to zero. Add 6 to both sides.
a 2, b 8, c 6
Identify a, b, and c. (ax2 bx c 0 is
standard form.
Write the formula.
Substitute a, b, and c.
Simplify. (PEMDAS)
Simplify. (PEMDAS)
Take the square root.
Separate into two problems ( and -).
Simplify.
6
Using the Quadratic Formula to Solve Quadratic
Equations

• Quadratic Formula

Set equation equal to zero. Add 2x9 to both
sides.
1
a 1, b 2, c 9
Identify a, b, and c. (ax2 bx c 0)
Write the formula.
Substitute a, b, and c.
Simplify. (PEMDAS)
Simplify. (PEMDAS)
Take the square root.
The square root of a negative number does not
have a real number solution. It is what we call
a complex number. No Solution!!
7
10.8 Using the Discriminant with Quadratic
Equations

• The Discriminant (Tells you how many solutions
  to expect)
• No solution if
• One solution if
• Two solutions if
• Examples
• Give the number of solutions for each
  equation.

a 1, b 2, c 10
a 1, b 0, c -9
a 1, b 2, c 1
2 Solutions
No Solution
1 Solution