i need help again with math i hate math!?

Question

 A punter kicked a punt that was in the air for a distance of 41 yards. The path of the football can be modeled by y=-0.035x^2+1.4x+1 where x is the distance (in yards) and y is the height (in yards) the football is kicked.

 a.) Does the graph open up or down? 

b.) Does the graph have a maximum value or a minimum value?

c.) Find the maximum height of the football.

Answer 1

OK, the standard form of a quadratic equation is:

y = ax² + bx + c

In your case, a = -0.035, b = 1.4, and c = 1:

y = -0.035x² + 1.4x + 1

1. Does it open up or down? Think about it. The ball goes up until it reaches its highest point then it comes back down. So the parabola shape it traces out opens down. You can tell this from the equation because the value of a (-0.035) is negative. Anytime the value of a is negative, the parabola opens down. When a is positive, the parabola opens up.
2. Does the parabola have a maximum or minimum value? Again the ball goes up until it reaches its highest point then it comes back down. The highest point is a maximum.
3. Find the maximum height of the football. The maximum point corresponds to the vertex of the parabola. Can you find the vertex? [HINT: The x value of the vertex is x = -b/2a. Plug in the values of b and a to find the x coordinate. Once you have the x-coordinate of the vertex, plug it into the equation for the ball's height (they equation above) to find the maximum height.]

Answer 2

The parabola opens down because the leading coefficient is negative.

Because it opens down, it will have a maximum point.

To find the maximum height, you need to find the vertex of the parabola.

y = -0.035x² + 1.4x +1

The x-coordinate is found by -b/2a =

-1.4 / 2(-0.035) = 1.4/0.07 = 20

Plug 20 back into your equation.

y = -0.035(20)² + 1.4(20) +1

y = -14 + 28 + 1

y = 15

The vertex of the parabola is (20,15)

15 yards is the maximum height the football reaches.