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Question 63873: Please help me find the soultion of this word problem :
Erica has a difficult golf shot to make. Her ball is 120m from the hole. She wants the ball to land 10m in front of the hole, so it can roll to the hole. A 15m tree is two thirds the way between her ball and the hole.
a) Choose the base of the tree as the origin, write an algebraic equation to model the height of the ball to just clear the top of th tree, in 1) factored form 2) vertex form.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Erica has a difficult golf shot to make. Her ball is 120m from the hole. She wants the ball to land 10m in front of the hole, so it can roll to the hole. A 15m tree is two thirds the way between her ball and the hole.
a) Choose the base of the tree as the origin, write an algebraic equation to model the height of the ball to just clear the top of th tree,
Draw the picture: The y-intercept is at (0,15)
The x-intercepts are (-80,0) and (30,0)
1) factored form
y=k(x+80)(x-30)
When x=0 y=-2400k=15
k= -1/160
EQUATION:
y=(-1/160)(x+80)(x-30)
2) vertex form.
-160y = x^2+50x-2400
Complete the square to get:
-160y + 2400 + 625 = x^2+50x+625
-160y+3025=(x+25)^2
-160(y-18.9)=(x+25)^2
y-18.9 = (-1/160)(x+25)^2
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Cheers,
Stan H.
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