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UNIT 3 Stuff about quadratics
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WHAT DO YOU DO IF YOU SEE A NEGATIVE UNDER THE RADICAL?
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IMAGINARY UNIT
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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
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IMPORTANT RULE If I take the square root of both sides of an equation, then I must consider the positive and negative solution.
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SOLVE BY COMPLETING THE SQUARE Get the x and x² by itself Factor out 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
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VERTEX FORM Y=a(x – h)² + k
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WHAT IS THE AXIS OF SYMMETRY It is the line that cuts the parabola in half The equation is: x = the x coordinate of the vertex. Ex: y = (x – 4)² + 3 The axis of symmetry is: x = 4
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HOW DO I FIND THE Y-INTERCEPT Let x = 0 and solve for y!
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WHAT IS THE QUADRATIC FORMULA
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WHAT IS THE DISCRIMINANT? b² - 4ac
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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)
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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.
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PARABOLA
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INFORMATION ABOUT THE PARABOLA
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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
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