Exencises 1.2 Quadratic x es/865128/assignments/8194344 k 1.2: Quadratic Functio
ID: 3198042 • Letter: E
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Exencises 1.2 Quadratic x es/865128/assignments/8194344 k 1.2: Quadratic Functions Jennifer Zamora Show Intro/Instructions The height y (in feet) of a ball thrown by a child is /101 10) 10) 10) 10) 10) /10) /10) /10) 0/10) 14 where a is the horizontal distance in feet from the point at which the ball is thrown (a) How high is the ball when it leaves the child's hand? (b) What is the maximum height of the ball? (c) How far from the child does the ball strike the ground Preview feet Preview feet Preiew feet to/10 Get help: Video o/10) 0/10) 0/10) (0/10) (0/10) (0/10) 10: 10) (0/10) (0/10) Points possible: 10 This is attempt 1 of 3. Submit .2/200 rstonExplanation / Answer
y = (-1/14) x2 + 2x + 3
(a) When x = 0,
y = (-1/14) * 0 + 2 * 0 + 3
= 3 ft.
(b) Differentiating with respec to x
=> dy/dx = (-1/14) * 2x + 2 = -x/7 + 2
d2y/dx2 = -1/7 < 0
Therefore, there is a maximum at dy/dx = 0
=> -x/7 + 2 = 0
=> -x/7 = -2
=> x = 2*7
=> x = 14 ft.
(c) y = 0
=> (-1/14)x2 + 2x + 3 = 0
=> x2 - 28x - 42 = 0
=> x = [28 +/- sqrt(28*28 + 4*42)] / 2
=> x = 29.4272 or -1.4272
Since distance cannot be negative,
x = 29.4272 or 29.43 ft.
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