A: To find the height of the toy after 1 second, plug in t=1 into the equation:
h = -2(1)^2 + 7(1) + 4
h = -2 + 7 + 4
h = 9 feet
So, after 1 second, the toy is 9 feet high.
B: To find the toy's max height, we need to find the vertex of the parabolic equation. The formula for the x-coordinate of the vertex of a parabolic equation in the form ax^2 + bx + c is given by x = -b/2a. In this case, a=-2 and b=7.
x = -7 / 2(-2)
x = -7 / -4
x = 1.75
Now, plug in t=1.75 into the equation to find the max height:
h = -2(1.75)^2 + 7(1.75) + 4
h = -2(3.0625) + 12.25 + 4
h = -6.125 + 12.25 + 4
h = 10.125 feet
Therefore, the toy's max height is 10.125 feet.
C: The toy is in the air from when it is thrown until it hits the ground, so we need to find the time it takes for h=0. Set h=0 in the equation and solve for t:
0 = -2t^2 + 7t + 4
0 = -2t^2 + 7t + 4
0 = (-2t - 1)(t - 4)
This gives us two possible solutions: t=-1/2 and t=4. Since time cannot be negative, the toy is in the air for 4 seconds.
Therefore, the toy is in the air for 4 seconds.
Your nephew is standing on his deck, which is 4 feet off the ground. He tosses his toy up into the air at an initial velocity of 7 feet per second. The equation h= -2t^2+7t+4 models the toy's height h in feet from the ground at t seconds after he threw it.
A: How high is the toy after 1 second?
B: What is the toy's max height?
C: How long is the toy in the air?
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