Quadratic Formula's and Completing The Square
2)How to use the given terms to find a full equation.
3)What to do in a situation where only the vertex is given with a parabola.
What are Quadratic Formula's?
The quadratic formula is used to find any x-intercept of a parabola.
There are values in the formula (a, b and c) these are all in a a quadratic equation
A standard form for quadratic equation is
The second step was substituting the variables into the quadratic equation form.
The next step to solve.
you are left with 2 x-intercepts.
What is a Discriminant?
If D<0, there are no x-intercepts.
If D>0, there are 2 x-intercepts.
If D=0, there are no x-intercepts.
In every quadratic formula there is a discriminant of #
The discriminant can be represented by:
In quadratic formula's there are these equations called a discriminant.
The discriminant is:
a)Write an equation to represent Matthew's total sales revenue.
Let X represent the amount of price by decrease.
b) What price must Matthew charge in order to maximize the total profits.
=200 + 20x - 5x - 0.5x^2 15/2=-7.5 7.5^2=56.25
=-(0.5x^2+15x) + 200
=-(0.5x^2 - 15x) + 200
=-(0.5x^2 - 15x + 56.25 - 56.25) + 200
=-(0.5x^2 - 15x + 56.25) + 200 + 56.25
=-(0.5^2 - 7.5)^2 + 256.25
This becomes a vertex of (7.5, 256.25)
Price= 10 - 0.50x
=10 - 0.50(7.5)
=10 - 3.75
Therefore, To get top dollar for his revenue. Matthew must charge $6.25 per card.