1. Solving Quadratic equations by graphing.
9-2 Algebra 1 Notes
Solving Quadratic equations by graphing.

2. 9-2 pg e, 57-75(x3)

3. Example 1: Two Roots Solve 𝑥 2 −3𝑥−10=0 by graphing. 12 10 8 6 4 2 -10-8 -6 -4 -2
Solve 𝑥 2 −3𝑥−10=0 by graphing.

4. Example 1: Two Roots
Solve 𝑥 2 −3𝑥−10=0 By graphing. 𝑥= − −3 2 1 𝑥= 3 2 𝑥=−2, 5 8 6 4 2
-10 -8 -6 -4 -2 10 12
-12
-14 𝒙 𝒚
−10 1
−12
3 2
−12.25 2 3

5. Example 2: Double Root Solve 𝑥 2 +8𝑥=−16 By graphing. 20 18 16 14 1210 8 6 4 2 -9 -8 -7 -6 -5 -4 -3 -2 -1 1
Solve 𝑥 2 +8𝑥=−16 By graphing.

6. Example 2: Double Root 20 18 16 14 12 10 8 6 4 2 -9 -8 -7 -6 -5 -4 -3 -2 -1 1
Solve 𝑥 2 +8𝑥=−16 By graphing. 𝑥= − 𝑥=−4 𝑥=−4 𝒙 𝒚 −6 4 −5 1 −4 −3 −2

7. Example 3: No Real Roots Solve 𝑥 2 +2𝑥+3=0 by graphing. 10 9 8 7 6 5 4-5 -4 -3 -2 -1
Solve 𝑥 2 +2𝑥+3=0 by graphing.

8. Example 3: No Real Roots 10 9 8 7 6 5 4 3 2 1 -5 -4 -3 -2 -1
Solve 𝑥 2 +2𝑥+3=0 by graphing. 𝑥= − 𝑥=−1 𝑥=∅ 𝒙 𝒚 −3 6 −2 3 −1 2 1

9. Example 4: Approximate Roots with a table7 6 5 4 3 2 1 -3 -2 -1 8 -4
Solve 𝑥 2 +6𝑥+6=0 By graphing.

10. Example 4: Approximate Roots with a table7 6 5 4 3 2 1 -3 -2 -1 8 -4
Solve 𝑥 2 −4𝑥+2=0 By graphing. 𝑥= − −4 2 1 𝑥=2 𝑥=0.6, 3.4 𝒙 𝒚 2 1 −1 −2 3 4

11. Example 5: Approximate Roots with a Calculator
MODEL ROCKETS Consuela built a model rocket for her science project. The equation ℎ=−16 𝑡 𝑡 models the flight of the rocket launched from ground level at a velocity of 250 feet per second, where ℎ is the height of the rocket in feet after 𝑡 seconds. Approximately how long was Consuela’s rocket in the air?

12. Example 5: Approximate Roots with a Calculator
MODEL ROCKETS Consuela built a model rocket for her science project. The equation ℎ=−16 𝑡 𝑡 models the flight of the rocket launched from ground level at a velocity of 250 feet per second, where ℎ is the height of the rocket in feet after 𝑡 seconds. Approximately how long was Consuela’s rocket in the air? 15.6 𝑠𝑒𝑐𝑜𝑛𝑑𝑠