SOLUTION: The height (in feet) of a football kicked from the 30 yd line can be modeled by the equation h= -0.02x^2 + 1.2x, where x is the horizontal distance traveled in yards. Use calculato

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The height (in feet) of a football kicked from the 30 yd line can be modeled by the equation h= -0.02x^2 + 1.2x, where x is the horizontal distance traveled in yards. Use calculato      Log On


   

Question 1028883: The height (in feet) of a football kicked from the 30 yd line can be modeled by the equation h= -0.02x^2 + 1.2x, where x is the horizontal distance traveled in yards. Use calculator to answer the question
1.) On what yard line will the ball hit the ground?
2.) Will the football reach a height of 20 ft?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+h+=+-.02x%5E2+%2B+1.2x+
+h+ is in feet
+x+ is in yds
-----------------
(1)
The ball hits the ground when +h+=+0+
+-.02x%5E2+%2B+1.2x+=+0+
+x%2A%28+-.02x+%2B+1.2+%29+=+0+
+-.02x+%2B+1.2+=+0+
+.02x+=+1.2+
+x+=+1.2+%2F+.02+
+x+=+60+
The ball hits the ground on the 60 yd line
-----------------
(2)
+h+=+20+
The maximum height is at:
+x%5Bmax%5D+=+-b%2F%282a%29+
where:
+h+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
+a+=+-.02+
+b+=+1.2+
+c+=+0+
------------------
+-b%2F%282a%29+=+-1.2+%2F+%28+2%2A%28-.02%29+%29+
+-b%2F%282a%29+=+30+
+x%5Bmax%5D=+30+
Plug this back into equation
+h%5Bmax%5D+=+-.02x%5E2+%2B+1.2x+
+h%5Bmax%5D+=+-.02%2A30%5E2+%2B+1.2%2A30+
+h%5Bmax%5D+=+-18+%2B+36+
+h%5Bmax%5D+=+18+ ft
No, the ball will not reach 20 ft high
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Here's the plot:
+graph%28+500%2C+500%2C+-6%2C+70%2C+-3%2C+35%2C+-.02x%5E2+%2B+1.2x+%29+