This week in precalc we learned many things. We had to remember many things in order to successfully graph a quadratic equation.
- Convert between standard, general and factored form
- Standard form (vertex form) – vertex, line of symmetry, stretch value, opens up or down
- General form – y intercept (0,y), stretch value, opens up or down
- Factored form – roots (x- intercepts) (x,0), stretch value, opens up or down – > line of symmetry (find the average of the roots) ->the x value of the vertex
- ** factored form there needs to be integers rather than fractions
- a, p and q transform the graph
- a->stretch value, negative -> opens down, positive -> opens up
- A is a proper fraction 1/2 – compression – gets fatter
- A Is larger than 1 – stretch – gets skinnier
- P – horizontal translation (slide) (x-2) -> right (x+5) …. (x –5) -> left
- Q – vertical translation (slide) positive – > up negative -> down
- Maximum (opening down) and minimum (opening up) …. Vertex (y value or q)
- Standard graphing pattern … 1 3 5 …. So if a = 2 2 6 10
- Domain …all the values for x that you could plug into the formula …….
X E Real
- Range – all the possible y values y > minimum or y< maximum
- Completing the square – changes general form into vertex form
- Factor a trinomial …if it factors – nice roots
- If doesn’t factor …. Quadratic formula … discriminant …
- Table of values to graph
- Develop an equation from a word problem. modeling
These are key things in order to succeed in this chapter.