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Unit+7 1
 

Unit+7 1

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    Unit+7 1 Unit+7 1 Presentation Transcript

    • x
      –2
      –1
      0
      1
      2
      y
      6
      3
      2
      3
      6
      7-1
      PLUG IT IN, PLUG IT IN
      Warm Up
      1. Evaluate x2 + 5x for x = 4 and x = –3.
      36; –6
      2. Generate ordered pairs for the function y = x2 + 2 with the given x VALUES.
      {–2, –1, 0, 1, 2}
    • QUADRATIC FUNCTIONSAND THEIR GRAPHS
      NC GOAL: 4.02 Graph, factor, and evaluate quadratic functions to solve problems.
      7-1
    • ESSENTIAL QUESTIONS
      • WHAT IS THE STANDARD FORM OF A QUADRATIC FUNCTION?
      • WHAT IS A “VERTEX”?
      • WHAT ROLE WOULD AN “AXIS OF SYMMETRY” PLAY?
      • HOW IMPORTANT ARE THE SOLUTIONS?
      • WHAT EXACTLY ARE SOLUTIONS TO A QUADRATIC FUNCTION?
      • WHAT IS A “PARABOLA”?
      • WHAT CAN THE LEADING COEFFICIENT IN A QUADRATIC FUNCTION TELL ME?
      7-1
    • VOCABULARY
      PARABOLA
      VERTEX
      SOLUTIONS
      AXIS OF SYMMETRY
      STANDARD FORM
      MAXIMUM
      MINIMUM
      7-1
    • BLOOMS
      Analysing
      Comparing
      Organising
      Deconstructing
      Attributing
      Outlining
      Finding
      Structuring
      Integrating
      7-1
       Can you break information into parts to explore understandings and relationships?
    • TLWBAT
      FIND THE VERTEX OF A QUADRATIC FUNCTION, AND IDENTIFY THE AXIS OF SYMMETRY AND SOLUTIONS.
      GRAPH A PARABOLA ON THE COORDINATE PLANE USING THE VERTEX, SOLUTIONS, AND OTHER ORDERED PAIRS.
      7-1
    • WHAT IS A “PARABOLA”?
      THE GRAPH OF A QUADRATIC FUNCTION
    • 7-1
      The graph of a quadratic function is a curve called a parabola. To graph a quadratic function, generate enough ordered pairs to see the shape of the parabola. Then connect the points with a smooth curve.
    • WHAT IS THE STANDARD FORM OF A QUADRATIC FUNCTION?
      ax2 + bx + c = 0
      BUT
      a= 0
    • WHAT IS A “VERTEX”?
      THE VERTEX IS THE HIGHEST OR LOWEST POINT ON THE GRAPH.
      NOTE: A POINT IS AN (x,y) COORDINATE.
    • LETS TALK MAX AND MIN
      A PARABOLA HAS EITHER A MAXIMUM POINT
      OR A MINIMUM POINT, ALSO KNOWN AS THE
      VERTEX
      MAXIMUM POINT/HIGHEST POINT
      MINIMUM POINT/LOWEST POINT
    • WHAT CAN THE LEADING COEFFICIENT IN A QUADRATIC FUNCTION TELL ME?
      IF THE LEADING COEFFICIENT IS POSITIVE, THE GRAPH SMILES.
      IF THE LEADING COEFFICIENT IS NEGATIVE, THE GRAPH FROWNS.
      2x2 + 3x – 4
      MINIMUM POINT
      -2x2+ 3x – 4
      MAXIMUM
      POINT
    • 7-1
    • A.
      B.
      7-1
      Example 1: Identifying the Vertex and the Minimum or Maximum
      Identify the vertex of each parabola. Then give the minimum or maximum value of the function.
      The vertex is (–3, 2), and the minimum is 2.
      The vertex is (2, 5), and the maximum is 5.
    • a.
      b.
      7-1
      Check It Out! Example 2
      Identify the vertex of each parabola. Then give the minimum or maximum value of the function.
      The vertex is (3, –1), and the minimum is –1.
      The vertex is (–2, 5) and the maximum is 5.
    • WHAT IS THE “AXIS OF SYMMETRY”?
      THE IMAGINARY LINE DOWN THE MIDDLE OF THE PARABOLA MAKING BOTH SIDES MIRROR IMAGES.
      AXIS OF SYMMETRY
      THE AXIS OF SYMMETRY IS ALWAYS THE x VALUE IN THE VERTEX.
    • WHAT EXACTLY ARE SOLUTIONS TO A QUADRATIC FUNCTION?
      THE SOLUTIONS ARE THE X VALUES WHERE THE PARABOLA CROSSES THE x AXIS.
      I AM A SOLUTION
      SO AM I
    • A quick review on plotting points
      • The first number in an ordered pair is your x value and the second one is the y value.
      • Example: (2,3)
      x,y
      You move left and right to graph an x value and
      up and down to graph a y value. Lets try a few.
      ALWAYS BEGIN FROM THE ORIGIN
    • http://mathforum.org/cgraph/cplane/pexample.html
      INTERACTIVE FUN
      http://www.webmath.com/gpoints.html
      7-1
    • TODAY WE WILL LEARN HOW TO FIND THE VERTEX IN THE CALCULATOR
      • Lets use the function 3x2 + 5x + 5. Put this in your calculator under y=.
      • Push 2nd, trace, : notice #3 and 4? What does our graph have? Push 3 NOW IT GETS TRICKY
      • USE YOUR ARROWS TO MOVE TO THE LEFT OF THE VERTEX, STAY VERY CLOSE THOUGH, AND HIT ENTER. NOW MOVE TO THE RIGHT OF THE VERTEX, BUT STAY CLOSE, AND HIT ENTER 2 TIMES.
      • THE ORDERED PAIR AT THE BOTTOM OF THE SCREEN IS YOUR VERTEX.
    • LETS TRY ANOTHER ONE
      • -x2 + 4x + 3 does this graph have a minimum
      point or a
      maximum point?
      2nd, trace, 4, left bound, enter, right bound,
      enter enter. And the vertex is:
      (2,7)
      Be sure to put the vertex in parenthesis or it is
      wrong.
    • Now find the solutions
      • Use 2nd, trace, 5, enter, enter, enter. Find both of them and write them down. We can now graph this parabola with this information. But what if we needed a few more points to make a good graph.
      • If you push 2nd graph you will have a gozillion points to choose from. Pick a few.
      • DRAW THIS GRAPH ON THE PAPER PROVIDED. BE SURE TO LABEL EVERYTHING.
    • x
      y
      –2
      6
      –1
      3
      0
      2
      1
      3
      2
      6
      7-1
      Check It Out! Example 3
      Use a table of values to graph each quadratic function.
      y = x2 + 2
      Make a table of values.
      Choose values of x and
      use them to find values
      of y.
      Graph the points. Then connect the points with a smooth curve.
    • 7-1
      x
      y
      –2
      –16
      –1
      –4
      0
      0
      1
      –4
      2
      –16
      Example 4: Graphing Quadratic Functions by Using a Table of Values
      Use a table of values to graph the quadratic function.
      y = –4x2
      Make a table of values.
      Choose values of x and
      use them to find values
      of y.
      Graph the points. Then connect the points with a smooth curve.
    • 7-1
      WORKTIME
      COMPLETE THE
      WORKSHEET
    • 7-1
      CLOSING
      WHAT IS THE STANDARD FORM OF A QUADRATIC FUNCTION?
    • 7-1
      CLOSING
      WHAT IS A “VERTEX”?
    • 7-1
      CLOSING
      WHAT CAN THE LEADING COEFFICIENT IN A QUADRATIC FUNCTION TELL ME?
    • 7-1
      CLOSING
      WHAT EXACTLY ARE SOLUTIONS TO A QUADRATIC FUNCTION?
    • 7-1
      CLOSING
      WHAT IS AN AXIS OF SYMMETRY?
    • 7-1
      CLOSING
      CAN YOU NOW FIND THE VERTEX OF A QUADRATIC FUNCTION, AND IDENTIFY THE AXIS OF SYMMETRY AND SOLUTIONS.
    • 7-1
      CLOSING
      CAN YOU GRAPH A PARABOLA ON THE COORDINATE PLANE USING THE VERTEX, SOLUTIONS, AND OTHER ORDERED PAIRS.