1. 9-61. Consider the functions f(x) = x 2 – 2x – 8 and g(x) = –2.5x – 3.

2. 9.2.2 SOLVING SYSTEMS OF EQUATIONS April 21, 2016

3. Objectives CO: SWBAT solve systems of equations involving quadratics. LO: SWBAT identify important features of linear and quadratic graphs from their equations.

4. 9-62. Using a graph to determine the intersection of two curves can be challenging when the point(s) of intersection are not where the grid lines intersect or are outside the visible portion of the graph. Therefore, it helps to have another method for determining the points of intersection. a. What algebraic methods have you used to solve systems of equations? Discuss with your team members. b. Use one of the methods you listed in part (a) to solve for the points of intersection of f(x) = x 2 – 2x – 8 and g(x) = –2.5x – 3. Carefully record your steps. Be sure to collaborate with your team and check your results along the way. Do your algebraic solutions match your graphical solutions from the previous problem? x 2 – 2x – 8 = –2.5x – 3 x 2 +.5x – 5 = 0 (x + 2.5)(x – 2) = 0 x = -2.5 x = 2 g(2) = –2.5(2) – 3 g(2) = -8 (2,-8) g(-2.5) = –2.5(-2.5) – 3 g(-2.5) = 3.25 (-2.5,3.25)

5. 9-63. Consider the equations y = x 2 and y = 2x – 5.

6. 9-64. HOW MANY INTERSECTIONS? When given a graph of two parabolas or a line and a parabola, it is usually easy to determine how many points of intersection they have. But how can you tell algebraically? Your Task: Use an algebraic method of your choosing to determine the point(s) of intersection, if any exist, for the system assigned to your team. Examine your solution and decide what it indicates about the graph of the system. That is, do the parabolas intersect once? Twice? Do they never intersect? Once you have solved your team’s system, sketch a graph to verify your conclusion. a.y = x 2 y = 2x – 1 b. y = x 2 – 5x + 6 y = –x 2 c. y = x 2 – 4x + 5 y = –x 2 + 4x – 1 d. y = x 2 – x – 2 y = x 2 + 2x + 1 e. y = x 2 – x – 2 y = x – 6 f. y = 2x 2 + 3x – 9 y = x – 5 one point: (1, 1)no points two points: (1, 2) and (3, 2) one point: (–1, 0) no points two points: (1, – 4) and (–2, –7)