Can you graph this quadratic function? Does punting a football from the 40-yard line mean it reached the end zone

Question

On fourth down, a team is just out of field goal range. The punter is called in to punt. To avoid kicking the ball into the endzone, the punter needs to kick the football high and short. This punt can be modeled by y 􏰀 􏰁0.088x²+2.5x+1, where x is the distance (in yards) the foot- ball is kicked and y is the height (in yards) the football is kicked.

1. Graph the quadratic function.

2. Find the greatest height of the football.

3. If the punter punted the ball from the 40-yard line, did the ball reach the endzone?

Answer 1

Hi Larry V.,

For the graph of the equation y = -0.088x² + 2.5x + 1, this is a parabola that opens downward. To get some points to graph it, when x = 0, y = 1, (0, 1). And when y = 0, you can use a calculator or use the quadratic formula, x = [-b±√(b²-4ac)]/2a.

x = [-2.5±√(2.5²-4*-0.088*1)]/(2*-0.088)

x = -0.395 and x = 28.804

Two more points (-0.395, 0) and (28.804, 0).

The vertex is x = b/2a = 2.5/(2*0.088) = 14.205

And y = -0.088*14.205² + 2.5*14.025 + 1 = 18.756

The vertex is at (14.205, 18.756). With these 4 points, you can graph the parabola that opens downward. You can round these figures to make your graph.

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The greatest height for the football is the y value of the vertex 18.756 yds.

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The ball lands at the x value above 28.804 yds so it does not reach the endzone.

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I hope this helps, Joe