1. Warm Up

2. Graphing Quadratic Functions

3. Graphing Quadratic Functions
Brainstorm everything you know about a quadratic function.

4. THE GRAPH OF A QUADRATIC FUNCTION
The parabola opens up if a>0 and opens down if a<0
y = x2
The parabola is wider than the graph of y = x2 if |a| < 1 and narrower than the graph of y = x2 if |a| > 1.
vertex
y = -x2
Axis of symmetry

5. STANDARD FORM Graph y = 2x2 -8x +6 a = 2, b = -8, c = 6.
Solution: The coefficients for this function
Since a>0, the parabola opens up.
The x-coordinate is: x = -b/2a
The y-coordinate is:
The vertex is
a = 2, b = -8, c = 6.
x = -(-8)/2(2)
x = 2
y = 2(2)2-8(2)+6
y = -2
(2,-2).

6. GRAPH
VERTEX:
AXIS OF SYMMETRY:
Y INTERCEPT:

7. VERTEX FORM OF QUADRATIC EQUATION
y = a(x - h)2 + k
The vertex is (h,k).
The axis of symmetry is x = h.

8. GRAPHING A QUADRATIC FUNCTION IN VERTEX FORM
Example y = -1/2(x + 3)2 + 4
VERTEX:
AXIS OF SYMMETRY:
Y INTERCEPT:

9. INTERCEPT FORM OF QUADRATIC EQUATION
y = a(x - p)(x - q)
The x intercepts are p and q.
The axis of symmetry is halfway between (p,0) and (q,0).

10. GRAPHING A QUADRATIC FUNCTION IN INTERCEPT FORM
Example y = -(x + 2)(x - 4).
VERTEX:
AXIS OF SYMMETRY:
Y INTERCEPT:
X INTERCEPT:

11. WRITING THE QUADRATIC EQUATION IN STANDARD FORM
(1). y = -(x + 4)(x - 9)
(2). y = 3(x -1)2 + 8
-x2 + 5x + 36
3x2 - 6x + 11