Write a quadratic equation

Question

An electronics store discovers that it can sell 5 televisions per day by pricing them at $1so When the televisions are on sale for $100, the store sells 10 of them every day. Write a linear equation to compare the price of a television, p, to the number sold, x. Then, write a quadratic equation to compare the revenue, m, from selling televisions to the number sold, x. Graph this quadratic equation.

Answer 1

To write in a linear equation it must be done in form y=mx+b (in this case p instead of y) So we must find the m (slope) and the b (y-intercept).

To find the slope we take the change in y divided by the change in x.

(150-100)/(5-10) => 50/-5 => m=-10

To solve for b we plug in either sale or normal price. For this example I will use normal price

p=-10x+b => 150=-10(5)+b => 150=-50+b => b=200

So the linear equaion is p=-10x+200

For the quadratic equation {y=a(x-h)^2 +k} we must have a vertex. Let's assume the vertex is at the original price and sales. Thus m=a(x-5)^2 +150. We must solve for a to complete the equation. We will do this by plugging in the sales price.

100=a(10-5)^2+150 =>100=a(5)^2 +150 => 100=25a=150 =>-50=25a => a=-2

Thus if it was a quadratic equation it would be: m=-2(x-5)^2 +150