Warm Up 1.) Graph the set of points (-2, 7), (-1, 4), (0, 1), and (1, -2). Which model is most appropriate for the set? (linear or exponential) 2.) Which.

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Presentation transcript:

Warm Up 1.) Graph the set of points (-2, 7), (-1, 4), (0, 1), and (1, -2). Which model is most appropriate for the set? (linear or exponential) 2.) Which kind of function best models the data? Use differences or ratios. xy

9.8 Systems of Linear and Quadratic Equations

Objective Solve systems of linear and quadratic equations.

Systems of Equations You can solve systems of linear and quadratic equations graphically and algebraically. There can be two solutions, one solution, or no solution.

Example 1 – Solving By Graphing What are the solutions of the system? Solve by graphing. y = x 2 + x + 2 y = x + 6

Example 2 – Using Elimination The equations y = 24x + 15 and y = -x x + 15 model the daily sales of two types of computers, where x is the number of days since the computers were put on sale. One what day was the same number of each computer sold.

Extra Example 2 Since opening day, attendance at Pool A has increased steadily, while at Pool B first rose and then fell. The equation for attendance at Pool A is modeled by y = 32x The equation for Pool B’s attendance is y = -x x On what day(s) was the attendance the same at both pools.

Example 3 – Using Substitution What are the solutions of the system? y = x 2 – 4x + 2 y = -x

Extra Example 3 What are the solutions of the system? y = 12x + 30 y = x x - 12

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Bellwork Quiz 1.) What are the solutions of x x + 32 = 0? Use the quadratic formula. 2.) What is the number of solutions of 4x x + 9 = 0? 3.) Graph the set of points (-2, 7), (-1, 4), (0, 1), and (1, -2). Which model is most appropriate for the set? (linear or exponential)

Warm Up 1.) Use elimination to solve the system: y = x 2 – 13x + 52 and y = -14x ) Use substitution to solve the system: y = x 2 – 6x + 9 and y = -x + 5

Assignment Pg. 590 – 592 (5, 6, 10, 17 – 20 all, 23 – 26 all, 30 – 33 all, 38 – 43 all, 47 – 50 all, 54 – 58 all)

Warm Up Solve each equation by completing the square. 1.) x 2 + 8x = ) t 2 – 4t – 165 = 0

Warm Up Use the quadratic formula to find the solutions. 1.) -3x 2 – 11x + 4 = 0 2.) 7x 2 – 2x = 8

Bellwork Quiz 1.) Use algebra to solve the system: y = x 2 – 6x + 9 and y = -x ) Solve the equation by completing the square: x 2 + 8x = ) Use the quadratic formula to solve: -3x 2 – 11x + 4 = 0