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1 answer:
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Answer:
- maximum height: 26.5 ft
- air time: 2.5 seconds
Step-by-step explanation:
I find the easiest way to answer these questions is to use a graphing calculator. It can show you the extreme values and the intercepts. The graph below shows the maximum height is 26.5 ft. The time in air is about 2.5 seconds.
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If you prefer to solve this algebraically, you can use the equation of the axis of symmetry to find the time of the maximum height:
t = -b/(2a) = -(40)/(2×-16) = 5/4
Then the maximum height is ...
h(5/4) = -16(5/4)² +40(5/4) +1.5 = -25 +50 +1.5 = 26.5 . . . feet
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Now that we know the vertex of the function, we can write it in vertex form:
h(t) = -16(t -5/4)² +26.5
Solving for the value of t that makes this zero, we get ...
0 = -16(t -5/4)² +26.5
16(t -5/4)² = 26.5
(t -5/4)² = 26.5/16 = 1.65625
Then ...
t = 1.25 +√1.65625 ≈ 2.536954
The cannon ball is in the air about 2.5 seconds.
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Answer:
<h2>GRAPH III</h2>Step-by-step explanation:
Look at the picture.
We have
y = x² - 4 → move the graph of x² 4 units down (the vertex is (0, -4))
x + y + 2 = 0 <em>subtracy x and 2 from both sides</em>
y = -x - 2 → move the graph of -x 2 units down (the y-intercept os -2)
Only graph III and IV meets these conditions.
The solution is the points of intersection of the graphs.
Therefore your answer is GRAPH III
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