SOLUTION: Ushna sits by the lake and throws a stone by it. The path of the stone is described by the equation h = 22t - 5t^2 where h is the height of the stone in metres at t seconds after i

Hi

h = 22t - 5t^2   Path of the stone is a parabola:

I. with y-intercept at Pt(0,0)

II.  Opening downward (Note: negative coefficient for the x^2 term)

Note: the vertex form of a parabola,  where(h,k) is the vertex

h = 22t - 5t^2 completing square to find the vertex

h = -5(t^2 - 22/5)

h = -5[(t - 11/5)-121/25]

h = -5( t - 11/5)^2 + 121/5  

Vertex (maximum point) is ( 11/5,121/5)or(2.2,24.2) 

Line of symmetry for this parbola being the perpendicular line x = 2.2

a) time to reach the maximum height is 2.2 sec

b) time to reach the surface of the lake: 0 = t(-5t + 22)  t = 22/5 = 4.4 sec

Sketching the graph to see the path the stone thrown takes:

I. Plot the Points: y-intercept Pt(0,0), vertex (2.2,24.2)

II. draw the vertical axis of symmetry  x = 2.2 and then Plot Pt(4.4,0)

III. Sketch the parabola opening downward using the axis of symmetry as a reference