You are going to buy doughnuts for your coworkers. You buy 2 boxes of glazed doughnuts for $3.99 each, 3 boxes of chocolate-cove
2 answers:
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Answer:
Part a) About 48.6 feet
Part b) About 8.3 feet
Part c) The domain is and the range is
Step-by-step explanation:
we have
This is a vertical parabola open downward (the leading coefficient is negative)
The vertex represent a maximum
where
x is the ball's distance from the catapult in feet
y is the flight of the balls in feet
Part a) How far did the ball fly?
Find the x-intercepts or the roots of the quadratic equation
Remember that
The x-intercept is the value of x when the value of y is equal to zero
The formula to solve a quadratic equation of the form
is equal to
in this problem we have
so
substitute in the formula
therefore
The ball flew about 48.6 feet
Part b) How high above the ground did the ball fly?
Find the maximum (vertex)
Find out the derivative and equate to zero
Solve for x
<em>Alternative method</em>
To determine the x-coordinate of the vertex, find out the midpoint between the x-intercepts
To determine the y-coordinate of the vertex substitute the value of x in the quadratic equation and solve for y
the vertex is the point (24.3,8.3)
therefore
The ball flew above the ground about 8.3 feet
Part c) What is a reasonable domain and range for this function?
we know that
A reasonable domain is the distance between the two x-intercepts
so
All real numbers greater than or equal to 0 feet and less than or equal to 48.6 feet
A reasonable range is all real numbers greater than or equal to zero and less than or equal to the y-coordinate of the vertex
so
we have the interval -----> [0,8.3]
All real numbers greater than or equal to 0 feet and less than or equal to 8.3 feet