1.  Hitting a golf ball out of a sand trap:  https://www.youtube.com/watch?v=FLR4V_lX JYE https://www.youtube.com/watch?v=FLR4V_lX JYE  The path of the ball can be approximated by: ◦ y = -x 2 + 5x ◦ x is the horizontal distance travelled by the ball in meters ◦ y is the height of the ball in meters What is the greatest height achieved by the ball?

2. Table of Values x012345 y046640 NOTICE: x values are all positive, since ball moves forward, not backward and a y- value of 0 is where the ball stops (ground level) So the maximum height is y = 6m, and it occurs for 2 seconds Wait, how can the maximum height occur for more than an instant? Perhaps there’s a more accurate way to see the maximum height

3.  Graph Using the graph, we can see the 2 points where maximum height of 6m occurs The maximum height actually occurs between these points, at x = 2.5, which is y = 6.25 A table of values is also correct, but you need more data points to have more accuracy

4. Sketch the graph of the relation y = x 2 – 6x. Determine the equation of the axis of symmetry, the coordinates of the vertex, the y- intercept and the x-intercepts.  Relationship is quadratic since highest degree is 2  a = 1(parabola opens upward), b = -6, c = 0  In order to sketch the graph, create a table of values and then plot the points

5. xy 7 00 1-5 2-8 3-9 4-8 5-5 60 77 Once you make your table of values, plot the points on a set of axes. Axis of Symmetry Equation of Axis of Symmetry: x = 3 Vertex Coordinates of Vertex: (3, -9)

6. xy 7 00 1-5 2-8 3-9 4-8 5-5 60 77 Locating the x and y intercepts. x-intercepts: when y = 0 (0,0) and (6,0) y-intercept: when x = 0 (0,0) You can either read this off the table of values, or see it from the graph.

7.  Pied Kingfisher catching fish in a split second https://www.youtube.com/watch?v=6YRM0sy3 xIY The underwater path of the bird is described by a parabola with the equation y = 0.5x 2 – 3x, where x is the horizontal position of the bird relative to its entry point, and y is the depth of the bird underwater (both in meters).

8.  The vertex of a parabola has the: ◦ Min y-value if parabola opens up ◦ Max y-value if parabola opens down  A parabola is symmetric with respect to a vertical line through its vertex  x-intercept is when y=0  y-intercept is when x=0