PLEASE HELP!!! This is a last minute homework help!!!
A computer software company models the profit on its latest video game using the relation: p(x) = -4x^2+20x-9, where x is the number of games produced in hundred thousands and p(x) is the profit in millions of dollars.
A) what type of function is p(x)?
b) what are the break-even points for the company? (break-even points means when profit is zero)
A) polynomial (quadratic, to be exact)
B) solve -4x^2+20x-9 = 0
using the quadratic formula or factoring or completing the square.
I'd be happy to help you with your homework! Let's break down the problem step by step.
A) To determine the type of function p(x) is, you need to analyze its equation. In this case, p(x) = -4x^2 + 20x - 9.
The equation is a second-degree polynomial, as indicated by the presence of the x^2 term. Polynomial functions are expressed in the form ax^n + bx^(n-1) + ... + k, where a, b, ..., k are coefficients, and n is a non-negative integer.
In our case, the highest power of x is 2, so the function is a quadratic function.
B) To find the break-even points when the profit is zero, we need to set p(x) equal to zero and solve for x.
So we have -4x^2 + 20x - 9 = 0.
Now we can use the quadratic formula: x = (-b ± √(b^2 - 4ac))/(2a), where the quadratic equation is in the form ax^2 + bx + c = 0.
For our equation, a = -4, b = 20, and c = -9. Plugging these values into the quadratic formula, we get:
x = (-20 ± √(20^2 - 4(-4)(-9))) / (2(-4))
Simplifying further:
x = (-20 ± √(400 - 144)) / (-8)
x = (-20 ± √256) / (-8)
x = (-20 ± 16) / (-8)
Now, we have two solutions:
x1 = (-20 + 16) / (-8) = -4/(-8) = 1/2
x2 = (-20 - 16) / (-8) = -36/(-8) = 9/2
Therefore, the break-even points for the company are x = 1/2 and x = 9/2 (or 0.5 and 4.5 when multiplied by 100,000).