Pls help me with thid
2 answers:
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Answer:
Part A) The vertex is the point (22,100) see the explanation
Part B) The x-intercepts are the points (12,0) and (32,0 see the explanation
Part C) The y-intercept is the point (0,-384) see the explanation
Step-by-step explanation:
Let
x ----> the number of cups of coffee sold
f(x) ---> the amount of profit
we have
This is a vertical parabola open downward (the leading coefficient is negative)
The vertex represent a maximum
Part A) Determine the vertex. What does this calculation mean in the context of the problem?
Convert the quadratic equation in vertex form
Factor -1
Complete the square
Rewrite as perfect squares
The vertex is the point (22,100)
That means ----> The maximum profit of $100 is when the number of cups of coffee sold is 22
Part B) Determine the x-intercepts. What do these values mean in the context of the problem?
we know that
The x-intercepts are the values of x when the value of the function is equal to zero
so
we have
For f(x)=0
solve for x
take square root both sides
so
The x-intercepts are the points (12,0) and (32,0)
That means -----> When the number of cups of coffee sold is 12 or 32 the profit is equal to zero
Part C) Determine the y-intercept. What does this value mean in the context of the problem?
we know that
The y-intercept is the value of the function when the value of x is equal to zero
so
For x=0
substitute the value of x
The y-intercept is the point (0,-384)
That means ----> When the number of cups of coffee sold is zero the profit is negative -$384 (the cost is greater than the revenue)