1. CHAPTER 6 SECTION 1 GRAPHING QUADRATIC FUNCTIONS

2. What is a Quadratic Function
A Quadratic function is any function where the degree of the equation is 2.

3. Components of a Quadratic Function
y = ax2 + bx + c
ax2 = quadratic term
bx = linear term
c = constant

4. Graph of a Quadratic Function is a Parabola

5. What do the parts tell us?
Axis of Symmetry – splits graph vertically
into 2 mirrored halves.
Vertex – Midpoint of graph, lies on the axis of symmetry,
and is the Maximum or Minimum of the graph.
Intercepts – c is the y-intercept and the graph may cross the x-axis 2, 1, or no times

6. Axis of Symmetry Standard Form of a quadratic. Axis of Symmetry is,
,also give you the x coordinate of the vertex.
Substitute x value into equation to find the y coordinate of the vertex.

7. Graphing with Tables x f(x) y 2 #’s Left 1 # left 1 # right
2 #’s Right

8. Minimum & Maximum y – coordinate of the Vertex.
a is negative
Minimum
a is Positive

9. Try:
State the direction of opening and whether the graph has a minimum or a maximum
Up; Minimum
Down; Maximum

10. Find: a.) The y-intercept, the equation for the axis of symmetry, and the x-coordinate of the vertex. y = -x2 + 4x – a = -1, b = 4, c = -1
y-intercept = c (the constant)
c = -1
y-intercept = -1
Equation for axis of symmetry
x-coordinate of vertex
(Same as axis of symmetry)
x-coordinate is 2.

11. Find: b) Make a table of values that includes the vertex.
f(x) y
-(0)2 + 4(0) – 1= -1 1
-(1)2 + 4(1) – 1= 2
-(2)2 + 4(2) – 1= 3
-(3)2 + 4(3) – 1= 4
-(4)2 + 4(4) – 1=

12. c) Graph the Function