Question

A punter kicked a 41-yard punt. The path of the football can be modeled by y = -0.035x^2 + 1.4x + 1, where x is the distance (in yards) the football is kicked and y is the height (in yards) the football is kicked. 1. Does the graph open up or down?2. Does the graph have a maximum value or a minimum value?3. Graph the quadratic function.4. Find the maximum height of the football. im really struggling.

Answer 1

Open down, Maximum value, attached image, y=15 yards

Explanation:

1) Open down. This can be figured out by the sign of the quadratic term (if negative open down if positive the parabola opens up). In this case -0.035 is negative

2) Maximum value. Since it opens down it has a maximum value

3) Attached image

4) In vertex form

y = -0.035x^2 + 1.4x + 1

y = -0.035(x^2 - 40x) + 1

y = -0.035[ (x - 20)^2 - 400) + 1

y = -0.035(x - 20)^2 + 15

For x=20 yards then y=15 yards (maximum yard). In the graph we can see that the max height is 15 yards also

Answer 2

The graph is a parabola and will open downwards.

It will have a maximum value.

To find the maximum value we convert to vertex form:-

y = -0.035x^2 + 1.4x + 1

y = -0.035(x^2 - 40x) + 1

y = -0.035[ (x - 20)^2 - 400) + 1

y = -0.035(x - 20)^2 + 15

The maximum height of the ball is 15 yards