L5-11 Quadratic Systems, (by graphing) Text pp 213 – 218 Workbook pp 183 – 188 Essential Question: Can I find the solutions to a system that involves a quadratic equation?

Warmup/Review: Simplify the following 1. −121 2. −12 3. (2 – 3i) – (3 + 4i) 4. (2 – 3i)(3+ 4i) 11i i 12 i 4 3 2i 𝟑 –1 – 7i 6 + 8i – 9i – 12i2 6 – i + 12 18 – i

Ex 1: Solving a Linear-Quadratic System Graphically Solve the system: y1 = x2 + 4x + 1 y2 = x + 1 Graph y1 with a table. x = –3 , y = –2 x = –2, y = –3 x = –1, y = –2 x = 0 , y = 1 x = 1 , y = 6 x = 2 , y = 13… Graph the linear equation: The y-intercept is 1 and the slope is 1. And (0, 1) is a solution Graph each equation and find the Points of Intersection. Any system that involves a quadratic can have up to two solutions (ordered pairs as answers). (–3, –2) is a solution

Ex 2: Solving a Linear-Quadratic System using the Calculator (Ti-84+) 5) When it says “Guess?” MOVE the curser to the specific point you are looking for and hit “enter” a last time. The coordinates of that point are now listed at the bottom. (Round your answer as needed.) Solve the system: y1 = –x2 + 9x – 6 y2 = ½ x + 2 Repeat the process for any other points of intersection. (7.42, 5.71) is the other solution 1) Input each equation into “y =“. Hit “Graph”. 2) Hit “2nd” “calc/trace” and choose “5: intersect” 3) Hit “enter” to select the first equation. 4) Hit “enter” again to select the second equation (1.08, 2.54) is a solution

Homework/Practice Linear-Quadratic Systems – Worksheet 1 Do (1 – 5)