Completing the Square:
(a+b)^2 = a^2+2ab-b^2
(x+3)^2 = x^2+3x+9
How to make it a perfect square, if it's not given:
Consider the following:y=x^2+ 8x+5
1. Put '5' outside of the bracket
2. Divide 'b' by 2 then square it. In this case it's 8.
(8/2)^2 = 16
Then the equation becomes y=(x^2+8x+16-16)+5
3.Move the negative 16 outside the bracket.
4.Write as squaring a binomial
Therefore the vertex is (-4,-11)
The Quadratic Formula:
Consider the Following:
All quadratic equations of the form ax^2+bx+c=0 can be solved using the quadratic equation.
This is the quadratic equation:
The values for the variables a,b, and c are taken from standard form quadratic equation.
Use the quadratic formula to solve for the X-Intercepts
We know that a=3, b=5, and c=2
1. Substitute in the values.
2. Add the vaules together in the square root.
3. Square root the result.
4. Add and subtract the outside number with the product of the square root.
5. Then divide the number you get from subtracting and adding with 2a.
Here is a video by mahalodotcom on Youtube on how to solve the quadratic formula.
The equation for the discriminant is:
If D>0 there are two x-ints
If D<0 there are no x-ints
If D=0 there is one x-int
Word Problem: Completing the square
let 'x' represent # of decreases
Therefore, Ms. Dhaliwal should change her price to $10.5 because she can maximize her profit to $441