Help me please it’s due today
1 answer:
Answer:
49 ft
Step-by-step explanation:
h(t) = 56t - 16t²
This is the equation of a parabola.
We must solve the equation to find the time (t) when the ball reaches its maximum height (h).
The coefficient of t² is negative, so the parabola opens downward, and the vertex is a maximum.
One way to solve this problem is to convert the equation to the vertex form.
We do that by completing the square.
Calculation:
h = -16t² + 56t
Divide both sides by -16 to make the coefficient of t² equal to 1.
(-1/16)h = t² - ⁷/₂t
Square half the coefficient of t
(-7/4)² = 49/16
Add and subtract it on the right-hand side
(-1/16)h = t² - ⁷/₂t + 49/16 - 49/16
Write the first three terms as the square of a binomial
(-1/16)h = (t - ⁷/₄)² - 49/16
Multiply both sides by -16
h = -16(t - ⁷/₄)² + 49
You have converted your equation to the vertex form of a parabola:
y = a(t - h)² + k = 0,
where (h, k) is the vertex.
h = ⁷/₄ and k = 49, so the vertex is at (⁷/₄, 49).
The time to reach maximum height is ⁷/₄ s = 1.75 s.
The graph below shows that the ball reaches a maximum height of 49 ft after 1.75 s.
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The attached graph represents the graph of f(x) = (x - 1)^2 - 2
<h3>How to plot the graph?</h3>The equation is given as:
f(x) = (x - 1)^2 - 2
Next, we set x to -2, -1, 0, 1 and 2.
So, we have:
f(-2) = (-2 - 1)^2 - 2 = 7
f(-1) = (-1 - 1)^2 - 2 = 2
f(0) = (0 - 1)^2 - 2 = -1
f(1) = (1 - 1)^2 - 2 = -2
f(2) = (2 - 1)^2 - 2 = -1
This means that the table of values is
x f(x)
-2 7
-1 2
0 -1
1 -2
2 -1
Next, we plot the above points and connect them.
See attachment for the graph of f(x) = (x - 1)^2 - 2
Read more about graphs and functions at:
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