1. Solving Quadratic Equations using the Quadratic Formula
9.5
Solving Quadratic Equations using the Quadratic Formula
Students will be able to solve quadratic equations using the Quadratic Formula.
Students will be able to interpret the discriminant.
Students will be able to choose efficient methods for solving quadratic equations.

2. Students will be able to solve quadratic equations using the Quadratic Formula.
By completing the square for the quadratic equation 𝑎 𝑥 2 +𝑏𝑥+𝑐=0, you can develop a formula that gives the solution of any quadratic equation in standard from.
This formula is called the Quadratic Formula.

3. Students will be able to solve quadratic equations using the Quadratic Formula.
The real solutions of the quadratic equation 𝑎 𝑥 2 +𝑏𝑥+𝑐=0 are
where 𝑎≠0 and 𝑏 2 −4𝑎𝑐≥0.

4. Students will be able to solve quadratic equations using the Quadratic Formula.
Solve 2 𝑥 2 −5𝑥+3=0 using the Quadratic Formula.
Remember
𝑎=2, 𝑏=−5, 𝑐=3
Plug into the Quadratic Formula

5. Students will be able to solve quadratic equations using the Quadratic Formula.

6. Students will be able to solve quadratic equations using the Quadratic Formula.
Solve 𝑥 2 −6𝑥+5=0 using the Quadratic Formula.
Remember
𝑎=1, 𝑏=−6, 𝑐=5
Plug into the Quadratic Formula

7. Students will be able to solve quadratic equations using the Quadratic Formula.

8. Students will be able to solve quadratic equations using the Quadratic Formula. You Try!!
Solve −3𝑥 2 +2𝑥+7=0 using the Quadratic Formula.
Remember
𝑎=−3, 𝑏=2, 𝑐=7
Plug into the Quadratic Formula

9. Students will be able to solve quadratic equations using the Quadratic Formula.

10. 2. Students will be able to interpret the discriminant.
The expression 𝑏 2 −4𝑎𝑐 in the Quadratic Formula is called the discriminant.
Because the discriminant is under the radical symbol, you can use the value of the discriminant to determine the number of real solutions of a quadratic equation and the number of x-intercepts of the graph of the related function.
𝑏 2 −4ac>0
Two real solutions
Two x-intercepts
𝑏 2 −4ac=0
One real solution
One x-intercept
𝑏 2 −4ac<0
No real solutions
No x-intercept

11. 2. Students will be able to interpret the discriminant.
Determine the number of real solutions of 𝑥 2 +8𝑥−3=0.
𝑏 2 −4ac= 8 2 −4∙1∙(−3)
=64− −12
=64+12
=76
The discriminant is greater than 0.
So, the equation has two real solutions.

12. 2. Students will be able to interpret the discriminant.
Determine the number of real solutions of 9 𝑥 2 +1=6𝑥.
Write the equation in standard form:
9 𝑥 2 −6𝑥+1=0
𝑏 2 −4ac= (−6) 2 −4∙9∙1
=36−36 =0
The discriminant equals 0.
So, the equation has one real solution.

13. 2. Students will be able to interpret the discriminant.
You Try!!
Determine the number of real solutions of 6 𝑥 2 +2𝑥=−1.
Write the equation in standard form:
6 𝑥 2 +2𝑥+1=0
𝑏 2 −4ac= (2) 2 −4∙6∙1
=4−24
=−20
The discriminant is less than 0.
So, the equation has no real solutions.

14. Methods for Solving Quadratic Equations.
3. Students will be able to choose efficient methods for solving quadratic equations.
Methods for Solving Quadratic Equations.
Method
Advantages
Disadvantages
Factoring
Straight forward when the equation can be factored easily
Some equations are not factorable
Using Square Roots
Use to solve equations of the form 𝑥 2 =𝑑
Can only be used for certain equations
Completing the Square
Best used when 𝑎=1 and 𝑏 is even
May involve difficult calculations
Quadratic Formula
Can be used for any quadratic equation
Gives exact solutions
Takes time to do calculations