1 Stuff about quadraticsUnit 4 Stuff about quadratics

2 What do you do if you see a negative under the radical?You Pull your “i” out. Ex. −16 =4𝑖 Ex. −7 =𝑖 7

3 Imaginary Unit −1 = i i² = -1

4 where (h, k) is the vertexVertex Form Y=a(x – h)² + k where (h, k) is the vertex

5 Standard Form f(x) = Ax² + Bx + C

6 How do I find the vertex? Identify the shift!Or x = -b/2a, then find y. Or 2nd Calc Min or Max!

7 IS THE GRAPH A MAXIMUM OR A MINUMUMThis is a maximum. This is a minimum.

8 What is the axis of symmetryIt is the line that cuts the parabola in half The equation is: x = the x coordinate of the vertex.

9 How do I find the y-interceptLet x = 0 and solve for y! Or 2nd CALC value x=0 enter

10 Ways to solve a quadratic EquationGraph and find the x-intercepts Use the Quadratic formula Complete the square Factor and set each factor equal to zero No middle term, just solve

11 Solve by completing the squareGet the x and x² by itself Divide by the lead coefficient, then introduce blanks to both sides Complete the square (you know take half… then square) Take the square root of both sides, then solve

12 What is the quadratic formula𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎

13 Important Rule If I take the square root of both sides of an equation, then I must consider the positive and negative solution.

14 What is the Discriminant?b² - 4ac

15 What does the discriminant tell us?If it’s positive and a perfect square, then 2 real rational roots If it’s positive and not a perfect square, then 2 real irrational roots If it’s zero, then 1 real rational root If it’s negative, then 2 complex roots (imaginary)

16 Special inequality ruleIf you multiply or divide both sides of an inequality by a negative number, then you flip the inequality sign.

17 Solve quadratic inequalitiesFind the roots of the quadratic. Establish a number line with the roots. Check values to see where x produces a true solution (yes or no). Write the solution.

18 parabola The set of all points in a plane that are the same distance from a given point called the focus and a given line called the directrix.

19 parabola

20 Information about the parabolaVertex Form y=a(x-h)² + k Vertex (h,k) Focus ℎ,𝑘+ 1 4𝑎 Directrix 𝑦=𝑘− 1 4𝑎

21 Quadratic Data STAT EDIT enter: enter the x’s in L1 and the y’s in L2STAT CALC 5:Quadreg enter**, VARS, over to Y-VARS, enter, enter, then enter again. Turn the STAT PLOT on: 2nd y= Zoom 9 to see data or Zoom 0 **NEWER CALCULATORS: When you do STAT CALC, on the line STORE RegEQ go VARS, over to YVARS, enter, enter