UNIT 4 Stuff about quadratics

WHAT DO YOU DO IF YOU SEE A NEGATIVE UNDER THE RADICAL?

IMAGINARY UNIT

WAYS TO SOLVE A QUADRATIC EQUATION  Graph 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

IMPORTANT RULE  If I take the square root of both sides of an equation, then I must consider the positive and negative solution.

SOLVE BY COMPLETING THE SQUARE  Get 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

VERTEX FORM  Y=a(x – h)² + k

STANDARD FORM  f(x) = Ax² + Bx + C

WHAT IS THE AXIS OF SYMMETRY

HOW DO I FIND THE Y-INTERCEPT  Let x = 0 and solve for y!

WHAT IS THE QUADRATIC FORMULA

WHAT IS THE DISCRIMINANT?  b² - 4ac

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)

SPECIAL INEQUALITY RULE  If you multiply or divide both sides of an inequality by a negative number, then you flip the inequality sign.

SOLVE QUADRATIC INEQUALITIES  Find 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.

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.

PARABOLA

INFORMATION ABOUT THE PARABOLA

QUADRATIC DATA  STAT EDIT enter: enter the x’s in L1 and the y’s in L2  STAT CALC 5:Quadreg enter**, VARS, over to Y-VARS, enter, enter, then enter again.  Turn the STAT PLOT on: 2 nd 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