Quadratics
by Chris Bradshaw
1. Graphing Quadratics
1.1. 1) Figure out the x and y intercepts
1.2. 2) Determine the vertex
1.3. 3) Determine if the parabola is positive or negative (arching up or arching down)
1.4. 4) Figure out at least two other points on each side of the vertex
1.5. 5) Draw graph once enough points are determined
2. Key Takeaways
2.1. There may be one solution
2.1.1. Ex: (x-3)(x-3)=0
2.2. The solutions may not be integers, therefore we will need to use the quadratic equation to determine the two solutions
2.3. The solutions may be in imaginary units
3. Factoring
3.1. 1) Use the FOIL Method (First, Outer, Inner, Last) to expand into quadratic form
3.1.1. Ex. (x-4)(x+3) = x^2-4x+3x-12
3.2. 2) To condense the Quadratic Equation, begin by listing all the factors of the last number (c term)
3.2.1. Ex: for x^2-4x-12=0: 1,2,3,4,6,and 12
3.3. 3) Determine what two factors can add up to the middle x term (b term)
3.3.1. Ex: x^2-4x-12=0, what two factors will get us -4? What about -6 and 2?
3.4. 4) After determining the factors, we can set up the quadratic
3.4.1. Ex: (x-6)(x+2)=0
3.5. 5) From here, we can figure out the key x coordinates of the quadratics
3.5.1. Ex: x=6 and x=-2