9514 1404 393
Answer:
E. 36.8 ft
F. 59 ft
G. 3.5 ft or 114.5 ft
Step-by-step explanation:
E. Put x=60 in the equation and do the arithmetic.
h = -0.01·60^2 +1.18·60 +2 = -36 +70.8 +2 = 36.8
The height is 36.8 feet when the ball is 60 feet downfield.
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F. The vertex of expression ax^2 +bx +c is x = -b/(2a). Here, that is ...
x = -(1.18)/(2(-0.01)) = 59
The ball has traveled 59 feet downfield when it reaches its maximum height.
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G. To find the downfield distance for a height of 6 feet, we set h=6 and solve for x.
6 = -0.01x^2 +1.18x +2
0.01x^2 -1.18x +4 = 0 . . . put in standard form
x^2 -118x +400 = 0 . . . . . multiply by 100 to get rid of decimals
x = (118 ± √(118² -4(1)(400)))/(2) = 59 ±√3081
x ≈ 59 ± 55.5 ft = {3.5 ft, 114.5 ft}
The ball will be 6 ft high at distances of 3.5 and 114.5 ft downfield.
