1. 5.1 GRAPHING QUADRATIC FUNCTIONS I can graph quadratic functions in standard form. I can graph quadratic functions in vertex form. I can graph quadratic functions in intercept form. You NEED graph paper today!

2. QUADRATIC FUNCTION?  We’ve been working with functions in the form y = mx + b.  This was called a linear function because the graph was a straight line.  A quadratic function is the form:  y = ax 2 + bx + c where a ≠ 0  The graph of a quadratic function is:  A parabola What’s different between a linear function and a quadratic function?

3. QUADRATIC FUNCTION IN STANDARD FORM Y = AX 2 + BX + C  Vertex  Can either be the minimum of the parabola or the maximum of the parabola.  If a is positive…  The parabola goes up (like a cup)  If a is negative…  The parabola goes down (like a frown)

4. QUADRATIC FUNCTION Y = AX 2 + BX + C  Axis of symmetry  Parabolas are always symmetric.  Makes a vertical ‘imaginary’ line at the x coordinate of the vertex that cuts the parabola into equal halves.

5. EXAMPLE 1: GRAPHING A QUADRATIC FUNCTION IN STANDARD FORM Standard Form: y = ax 2 + bx + c  y = 2(2) 2 – 8(2) + 6  y = 2(4) – 16 + 6  y = 8 -10  y = -2 (2, -2)

6.  Axis of Symmetry:  x = 2  You also need two more points to be able to make the graph.  Choose x = 3 and x = 4 because they are right after the Axis of Symmetry  y = 2(3) 2 – 8(3) + 6  y = 2(9) – 24 + 6  y = 18 – 24 + 6  y = 0  (3, 0)  y = 2(4) 2 – 8(4) + 6  y = 2(16) – 32 + 6  y = 32 – 32 + 6  y = 6  (4, 6)

7.  Vertex: (2, -2)  Axis of Symmetry:  x = 2  Points:  (3,0)  (4,6)

8. INDIVIDUAL PRACTICE ON GRAPHING QUADRATICS IN STANDARD FORM  Pg 253  20-25  List the vertex  Axis of symmetry  At least 2 extra points  You have 15 minutes to work on this section of problems.  I will do the next part of notes in 15 minutes.

9. QUADRATIC FUNCTION IN VERTEX FORM  y = a(x – h) 2 + k  Vertex:  (h,k)  Axis of Symmetry:  x = h  You still also need to find two more points to plot.

10. EXAMPLE 2: GRAPHING A QUADRATIC FUNCTION IN VERTEX FORM  y = -3(x + 1) 2 + 2  Vertex:  (-1,2)  Axis of Symmetry:  x = -1  Points:  (0,-1)  (1,-10)  x = 0  y = -3(0+1) 2 + 2  y = -3(1) 2 + 2  y = -3(1) + 2  y = -3 + 2  y = -1  x = 1  y = -3(1+1) 2 + 2  y = -3(2) 2 + 2  y = -3(4) + 2  y = -12 + 2  y = -10 Vertex Form: y = a(x – h) 2 + k

11.  Vertex:  (-1,2)  Axis of Symmetry:  x = -1  Points:  (0,-1)  (1,-10)

12. INDIVIDUAL PRACTICE ON GRAPHING QUADRATICS IN VERTEX FORM  Pg. 253  26-31  List the vertex  Axis of symmetry  At least 2 extra points  You have 15 minutes to work on this section of problems.  I will do the next part of notes in 15 minutes.

13. QUADRATIC FUNCTIONS IN INTERCEPT FORM  y = a(x – p)(x – q)  The x-intercepts are p and q.  The axis of symmetry is halfway between p and q.  The vertex is found by plugging the axis of symmetry back in to the function and solve for y.

14. EXAMPLE 3: GRAPHING QUADRATICS IN INTERCEPT FORM  y = -(x + 2)(x - 4)  X-intercepts:  -2 and 4  Axis of symmetry:  x = 1  Vertex:  (1,9)  x = 1  y = -(1+2)(1-4)  y = -(3)(-3)  y = -(-9)  y = 9 Intercept Form: y = a(x – p)(x – q)

15.  X-intercepts:  -2 and 4  Axis of symmetry:  x = 1  Vertex:  (1,9)

16. INDIVIDUAL PRACTICE ON GRAPHING QUADRATICS IN INTERCEPT FORM  Pg. 254  32-37  List the vertex  Axis of symmetry  Intercepts