1. Solving Quadratic Equations
Chapter 9

2. Solving Quadratic Equations by Graphing
I can solve quadratic equations by graphing.

3. Solving Quadratic Equations by Graphing
Core Concepts (page 283 in Student Journal)
Solving Quadratic Equations by Graphing
Write the equation in standard form, ax2 + bx + c = 0 (or a form you are comfortable graphing).
Graph the equation.
Find the x-intercepts if possible.

4. Solving Quadratic Equations by Graphing
Number of Solutions to a Quadratic Equation 2 solutions: the graph intersects the x-axis at 2 places 1 solution: the graph intersects the x-axis at 1 place (vertex is on the x-axis) no solutions: the graph does not intersect with the x-axis

5. Solving Quadratic Equations by Graphing
Examples (page 284 in Student Journal) Solve by graphing. #1) x2 + 4x = 0 #2) -x2 = -2x + 1 #9) x2 + 4 = 0

6. Solving Quadratic Equations by Graphing
Solutions #1) x = -4, x = 0 #2) x = 1 #9) no solution

7. Solving Quadratic Equations Using Square Roots
I can solve quadratic equations using square roots.

8. Solving Quadratic Equations Using Square Roots
Vocabulary (page 288 in Student Journal)
square root: inverse operation of squaring

9. Solving Quadratic Equations Using Square Roots
Core Concepts (page 288 in Student Journal)
Number of Solutions to a Quadratic Equation
2 solutions: when x2 = d and d > 0
1 solution: when x2 = d and d = 0
no solutions: when x2 = d and d < 0

10. Solving Quadratic Equations Using Square Roots
Examples (page 289 in Student Journal)
Solve the equation.
#1) x = 0 #2) x2 – 25 = 0
#3) x2 + 6 = 6 #5) 2x = 0
#9) 81x2 – 49 = -24 #15) (2x + 7)2 = 49

11. Solving Quadratic Equations Using Square Roots
Solutions
#1) no solution #2) -5, 5
#3) 0 #5) -6, 6
#9) -5/9, 5/9 #15) -7, 0

12. Solving Quadratic Equations by Completing the Square
I can solve quadratic equations by completing the square.

13. Solving Quadratic Equations by Completing the Square
Vocabulary (page 293 in Student Journal)
completing the square: the process of changing the expression x2 + bx into a perfect square trinomial by adding (b/2)2 to x2 + bx

14. Solving Quadratic Equations by Completing the Square
Core Concepts (page 293 in Student Journal)
Completing the Square
Divide b by 2
Square (b/2) from step 1
Add (b/2)2 from step 2 to x2 + bx
Factor x2 + bx + (b/2)2

15. Solving Quadratic Equations by Completing the Square
Examples (page 294 in Student Journal)
Solve the equation by completing the square.
#7) x2 – 8x = -15
#14) x2 + 14x – 10 = 0

16. Solving Quadratic Equations by Completing the Square
Solutions
#7) 3, 5
#14) , 0.68

17. Solving Quadratic Equations Using the Quadratic Formula
I can solve quadratic equations using the Quadratic Formula.

18. Solving Quadratic Equations Using the Quadratic Formula
Vocabulary (page 298 in Student Journal)
Quadratic Formula: if ax2 + bx + c = 0, then x = (-b + sqrt(b2 - 4ac))/2a and (-b - sqrt(b2 - 4ac))/2a
discriminant: the expression under the square root in the quadratic formula (b2 - 4ac)

19. Solving Quadratic Equations Using the Quadratic Formula
Core Concepts (page 298 in Student Journal)
Interpreting the Discriminant
If the discriminant is…
positive, then there are 2 solutions.
zero, then there is 1 solution.
negative, then there are no solutions.

20. Solving Quadratic Equations Using the Quadratic Formula
Examples (pages 299 and 300 in Student Journal)
Determine the number of solutions to the equation.
#8) -x2 + 6x + 3 = 0
#9) x2 + 6x + 9 = 0

21. Solving Quadratic Equations Using the Quadratic Formula
Solutions
#8) 2 solutions
#9) 1 solution

22. Solving Quadratic Equations Using the Quadratic Formula
Solve the equation using the Quadratic Formula.
#1) x2 – 10x + 16 = 0
#5) -3x2 + 5x – 1 = -7

23. Solving Quadratic Equations Using the Quadratic Formula
Solutions
#1) 2, 8
#5) -0.82, 2.49