Quadratic Function - PowerPoint

							Name:
Date:
Topic: Solving & Graphing Quadratic Functions
Warm-Up:
Factor
1. 49p2 – 100

2. 6d4 + 4d3 – 6d2 – 4d

Solve for x:
3. 2x2 + 13x + 6
Quadratic Function
 (y = ax 2 + bx + c)
                       Vocabulary:
1. Quadratic Parent Function

2. Parabola = the graph of a
   quadratic function is a U-
   shaped curved.

3. Axis of Symmetry – divide the
   graph into two halves

       The line of symmetry ALWAYS
         passes through the vertex.




                                      Continue
4. Vertex
    • Minimum – lowest point
       of the parabola
    • Maximum – the highest
       point of the parabola.     y


                                       Vertex
                                      Maximum




                                                x




                         Vertex
                        Minimum
y = x2
   a = 1, b = 0, c = 0
   Minimum point (0,0)
   Axis of symmetry      y=x2
    x=0
                 Finding the Line of Symmetry


When a quadratic function is in   For example…
standard form
                                  Find the line of symmetry of
      y=   ax2   + bx + c,             y = 3x 2 – 18x + 7
The equation of the line of
symmetry is                       Using the formula…
                      b
                   x                 x  18  18  3
                      2a                 2 3 6


                                  Thus, the line of symmetry is x = 3.
                 Finding the Vertex
We know the line of symmetry                    y = –2x 2 + 8x –3
always goes through the vertex.
                                     STEP 1: Find the line of symmetry
Thus, the line of symmetry
gives us the x – coordinate of                 x  b  8  8  2
                                                  2a 2(2) 4
the vertex.
                                     STEP 2: Plug the x – value into the
                                     original equation to find the y value.
To find the y – coordinate of the
vertex, we need to plug the x –                   y = –2(2)2 + 8(2) –3
value into the original equation.
                                                  y = –2(4)+ 8(2) –3

                                                    y = –8+ 16 –3
                                                         y=5

                                 Therefore, the vertex is (2 , 5)
       A Quadratic Function in Standard Form
   Let's Graph ONE! Try …           y

               y = 2x 2 – 4x – 1
STEP 1: Find the line of symmetry



STEP 2: Find the vertex

                                               x
STEP 3: Find the y-intercept
when x = 0.


STEP 4: Find two other points
and reflect them across the line
of symmetry. Then connect the
five points with a smooth curve.
 A Quadratic Function in Standard Form
                            y
y=   2x2   – 4x – 1




                                         x
What happen if we change
 the value of a and c ?


        y=3x2        y=4x2+3




        y=-3x2       y=-4x2-2
            Conclusion
          (y = ax 2+bx+c)

   When a is positive,      the graph concaves
                              downward.
   When a is negative,      the graph concaves
                              upward.
   When c is positive       the graph moves up.
   When c is negative       the graph moves
                              down.
      Other Methods

   By factoring

   By using the
    quadratic formula      b  b  4ac
                                 2
                        x
                                2a
Factoring Example


     X2 - 2x = 0
     Factor in order to      y=x2-2x
      solve the equation
      (Remember to ask
      yourself does the
      function have a GCF.
     Find the x intercept.
     Two solutions, x=0
      and x=2.
Find the Solutions



   y=x2-4
                     y=x2+2x-15




   y=-x2+5



                     y=-x2-1
Find the solutions




                     y=-x2+4x-1
    Group Work:                  Page 544 – 545
Group 1:   Group 3:   Group 5:      Group 7:
#7, #20    #9, #22    #11, #24      #13, #28

Group 2:   Group 4:   Group 6:      Group 8:
#8, #21    #10, #23   #12, #25      #14, #30

     Independent Work:
             Page 538 (8, 10)
               Page 546 (43)
             Page 549 (a, b, c)
     HLA#1:


 Page 538 (7, 8)
Page 544 (2, 3, 4)