SOLUTION: A ball is thrown upward and outward from a height of six feet. The height of the ball, f(x), in feet can be modeled by f(x)=-0.1x^2 + 0.7x + 6 a.) What is the maximum height

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A ball is thrown upward and outward from a height of six feet. The height of the ball, f(x), in feet can be modeled by f(x)=-0.1x^2 + 0.7x + 6 a.) What is the maximum height      Log On


   

Question 1026235: A ball is thrown upward and outward from a height of six feet. The height of the ball, f(x), in feet can be modeled by
f(x)=-0.1x^2 + 0.7x + 6
a.) What is the maximum height, and how far from where it was thrown does this occur?
b.) How far does the ball travel horizontally before hitting the ground?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When the form is:
+f%28x%29+=+ax%5E2+%2B+b%2Ax+%2B+c+, then
the formula for the x-value of
maximum height is:
+x%5Bmax%5D+=+-b%2F%282a%29+
+f%28x%29+=+-.1x%5E2+%2B+.7x+%2B+6+
+x%5Bmax%5D+=+-.7+%2F+%28+2%2A%28-.1+%29%29+
+x%5Bmax%5D+=+.7%2F.2+
+x%5Bmax%5D+=+7%2F2+
+x%5Bmax%5D+=+3.5+
------------------
Plug this back in to get
+f%287%2F2%29+=+-.1%2A49%2F4+%2B+4.9%2F2+%2B+6+
+f%287%2F2%29+=+-4.9%2F4+%2B+4.9%2F2+%2B+6+
+f%287%2F2%29+=+4.9%2F4+%2B+24%2F4+
+f%287%2F2%29+=+28.9%2F4+
+f%287%2F2%29+=+7.225+
------------------
The maximum height is 7.225 ft
This is 3.5 ft from where it was thrown
----------------
The ball hits the ground when +f%28x%29+=+0+
+f%28x%29+=+-.1x%5E2+%2B+.7x+%2B+6+
+-.1x%5E2+%2B+.7x+%2B+6+=+0+
+-x%5E2+%2B+7x+%2B+60+=+0+
+%28+-x+%2B+12+%29%2A%28+x+%2B+5+%29+=+0+
+x+=+12+
The ball hits the ground at 12 ft from
where it was thrown
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check:
Here's the plot:
+graph%28+400%2C+400%2C+-2%2C+15%2C+-2%2C+10%2C+-.1x%5E2+%2B+.7x+%2B+6+%29+