Draw a graph representing h = 1 + x - (x^2 over 40) where x metres is the horizontal distance travelled by the ball from the bat.

Question

The height, h metres, of a cricket ball after being struck by a batsman, is given by the equation; h = 1 + x - (x² over 40) ...where x metres is the horizontal distance travelled by the ball from the bat.

Draw a graph (using technology) to represent this information. Ensure the graph shows the x- incepts.

Answer 1

y = 0 along the x-axis (the ground). I start by multiplying everything by -40.

0 = x² -40x - 40

x = [40 ± √(-40)² - 4(1)(-40))]/(2(1)

x = [40 ± √(1600 + 160)]/2

x = [40 ± √1760]/2

x = [40 + 42]/2

x = 82/2

x = 41 m

x = [40 - 42]/2

x = -2/2

x = -1

The 2nd answer gives us the portion of the parabola behind the striking of the ball that would otherwise touch the x-axis, so we disregard. The ball hits the ground 41 meters away.

Remember that the y-axis represents where the bat strikes the ball, and x = 0 along the y-axis. I won't show the math but you hopefully see that if x = 0 that y = 1.

x = -b/2a = 40/2 = 20 m.

h = 1 + 20 - 20²/40

h = 21 - 400/40

h = 21 - 10

h = 11 m

So, your y-intercept is (0,1), the vertex is (20,11) and the x-intercepts are at -1 and 41. I would dot (or dash) the portion of the parabola to the left of the y-axis since it technically doesn't exist outside the problem itself.