In the table, x represents the age in years of a collectible baseball card, and y represents its value in dollars. Cost of a Pac
2 answers:
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Answer:
Part A) The graph in the attached figure (see the explanation)
Part B) 16 feet
Part C) see the explanation
Step-by-step explanation:
Part A) Graph the function
Let
h(t) ----> the height in feet of the ball above the ground
t -----> the time in seconds
we have
This is a vertical parabola open downward (the leading coefficient is negative)
The vertex is a maximum
To graph the parabola, find the vertex, the intercepts, and the axis of symmetry
<em>Find the vertex</em>
The function is written in vertex form
so
The vertex is the point (0,98)
Find the y-intercept
The y-intercept is the value of the function when the value of t is equal to zero
For t=0
The y-intercept is the point (0,98)
Find the t-intercepts
The t-intercepts are the values of t when the value of the function is equal to zero
For h(t)=0
square root both sides
therefore
The t-intercepts are
Find the axis of symmetry
The equation of the axis of symmetry in a vertical parabola is equal to the x-coordinate of the vertex
so
----> the y-axis
To graph the parabola, plot the given points and connect them
we have
The vertex is the point
The y-intercept is the point
The t-intercepts are
The axis of symmetry is the y-axis
The graph in the attached figure
Part B) How far is the artifact fallen from the time t=0 to time t=1
we know that
For t=0
For t=1
Find the difference
Part C) Does the artifact fall the same distance from time t=1 to time t=2 as it does from the time t=0 to time t=1?
we know that
For t=1
For t=2
Find the difference
so
The artifact fall 48 feet from time t=1 to time t=2 and fall 16 feet from time t=0 to time t=1
therefore
The distance traveled from t=1 to t=2 is greater than the distance traveled from t=0 to t=1
