Page 60 - Math 9-10 (2009)

FOUNDATIONS OF MATHEMATICS, GRADE 10, APPLIED (MFM2P) 59
connections between each algebraic representation and the graph [e.g., the y-intercept is c in the form y = x2 + bx + c; the x-intercepts are r and s in the form
y = (x – r)(x – s)] (Sample problem: Use a graphing calculator to compare the graphs of y = x2 + 2x – 8 and y = (x + 4)(x – 2). In what way(s) are the equations related? What information about the graph can you identify by looking at each equation? Make some conclusions from your observations, and check your conclusions with a different quadratic equation.).
Solving Problems by Interpreting Graphs of Quadratic Relations
By the end of this course, students will:
– solve problems involving a quadratic rela- tion by interpreting a given graph or a graph generated with technology from its equation (e.g., given an equation represent- ing the height of a ball over elapsed time, use a graphing calculator or graphing soft- ware to graph the relation, and answer questions such as the following: What is the maximum height of the ball? After what length of time will the ball hit the ground? Over what time interval is the height of the ball greater than 3 m?);
– solve problems by interpreting the signifi- cance of the key features of graphs obtained by collecting experimental data involving quadratic relations (Sample problem: Roll a can up a ramp. Using a motion detector and a graphing calculator, record the motion of the can until it returns to its starting position, graph the distance from the starting position versus time, and draw the curve of best fit. Interpret the meanings of the vertex and the intercepts in terms of the experiment. Predict how the graph would change if you gave the can a harder push. Test your prediction.).