write on inequality

Question

an outdoor golfing range has two decks. the top deck is 10 ft high. if a player hits a ball off the top deck with a 9-iron, the ball reaches its peak of 55 ft. From the ground,when it is 15 ft from the deck.

write a quadratic to model the parabolic arc of the golf ball, and write an inequality that describes when the ball is above the deck.

Answer 1

You can use the vertex form of a parabola: y=a(x-h)^2 +k, where (h,k) is the vertex of the parabola.

The vertex of a parabola is the graph's minimum or maximum point. In the case of the golf ball, which travels up before coming down, the vertex is a maximum. They give that point as (15, 55). If you substitute those values for h and k, you have: y=a(x-15)^2 +55. We always want x and y to be in our final answer, but what's a?

We can determine it using the other point provided. Since the ball is originally hit from a height of 10 feet, you can substitute (0,10) into your equation and solve for a.

10 = a(0-15)^2 + 55

10 = a (225) + 55

10 = 225a + 55

-45 = 225a

a = -0.2

y = -0.2(x-15)^2 + 55

(Note: If you need your answer to be in standard form, you can FOIL and simplify.)

Now that we have the equation, we can determine the inequality. The height of the deck is 10 feet. We know that the ball is 10 feet high when it's on the deck. It then travels higher until reaching a height of 55 feet before beginning its descent. At what distance from the deck does it return to a height of 10 feet?

10 = -0.2(x-15)^2 + 55

-45 = -0.2(x-15)^2

225 = (x-15)^2

±15 = x-15

x = 0, x = 30

The ball is at the height of the deck at x=30, and x = 0, so the ball is above the deck when 0<x<30.