SOLUTION: A placekicker kicks the football, which reaches a maximum height of 8 yards and lands 50 feet away. Assuming the football was at the origin when it was kicked, write and equation f

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A placekicker kicks the football, which reaches a maximum height of 8 yards and lands 50 feet away. Assuming the football was at the origin when it was kicked, write and equation f      Log On


   

Question 937418: A placekicker kicks the football, which reaches a maximum height of 8 yards and lands 50 feet away. Assuming the football was at the origin when it was kicked, write and equation for the height of the football.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You are given the points:
( 0,0 )
( 50,0 )
The max height occurs halfway
between the horizontal
co-ordinates, so you also have:
( 25,24 )
Note that +8+ yds = +24+ ft
-------------------------------
The equation is in the form:
+h%28x%29+=+-a%2Ax%5E2+%2B+b%2Ax+%2B+c+
( 0,0 )
+0+=+-a%2A0%5E2+%2B+b%2A0+%2B+c+
+c+=+0+
------------
( 50,0 )
+0+=+-a%2A50%5E2+%2B+b%2A50+
+2500a+=+50b+
+50a+=+b+
------------------
( 25,24 )
+24+=+-a%2A25%5E2+%2B+b%2A25+
+24+=+-a%2A625+%2B+25b+
+625a+=+25b+-+24+
----------------------
By substitution:
+625a+=+25%2A50a+-+24+
+625a+=+1250a+-+24+
+625a+=+24+
+a+=+.0384+
+b+=+50a+
+b+=+1.92+
--------------
+h%28x%29+=+-.0384x%5E2+%2B+1.92x+ answer
----------------------------
check:
Does it go through ( 50,0 ) ?
+h%2850%29+=+-.0384%2A50%5E2+%2B+1.92%2A50+
+h%2850%29+=+-.0384%2A2500+%2B+96+
+h%2850%29+=+-96+%2B+96+
OK
------------
Does it go through ( 25,24 )?
+h%2825%29+=+-.0384%2A25%5E2+%2B+1.92%2A25+
+h%2825%29+=+-24+%2B+48+
+h%2825%29+=+24+
OK