Question

A company makes and sells headphones. The

function R= - 5x² +65x + 700 gives the amount
of money the company expects to make when the
price of the headphones is x dollars. When this
function is graphed, the vertex is 6.5, 911.25).
What does the x-value 6.5 represent?

Answer 1

At 6.5 dollars price of each headphone the revenue will be maximum which is $911.25.

Explanation:

A company makes and sells headphones. The function R= - 5x² +65x + 700 gives the amount of money the company expects to make when the price of the headphones is x dollars.

Now, we can convert the parabolic function of revenue R(x), to vertex form.

So, R = - 5x² + 65x + 700

⇒ R = -5(x² - 13x + 6.5²) + 700 + 5 × 6.5²

⇒ R = - 5(x - 6.5)² + 911.25

⇒ 5(x - 6.5)² = - (R - 911.25)

⇒ (x - 6.5)² = - 0.2 (R - 911.25)

Therefore, the parabola has vertex at (6.5,911.25) and its axis is parallel to negative y-axis.

Hence, the function has maxima at point (6.5,911.25) point.

And hence the x-value represents at x = 6.5 dollars price of each headphone the revenue will be maximum which is $911.25. (Answer)