9.3 Graphing Quadratic Functions
9.3 Graphing Quadratic Functions
2
Standard Form: ax + bx + c (a≠0)
2
Vertex Form: y = a (x-h) + k (a≠0)
(where (h,k) is the vertex)
The graph is a parabola - U-Shaped Graph.
· If a is positive, it opens up and the vertex is a
minimum value
· If a is negative, it opens down and the vertex is
a maximum value
· If |a|>1, the graph is narrower than the parent
function (parent function is f(x) = x2)
· If |a|<1, the graph is wider than the parent
function (parent function is f(x) = x2)
· The axis of symmetry is a vertical line through
the vertex and has the equation x = h
a>0 (positive)
opens up
vertex:minimum point
a<0 (negative)
opens down
vertex:maximum point
Sketch a graph of the Quadratic Function
1. Rearrange the equation into vertex form
2. Plot the vertex
3. Plot other points by going both left and right
"over 1 up 1a"
"over 2 up 4a"
"over 3 up 9a"
Graph the equation:
y = (x + 4)2 - 9
9.3 Graphing Quadratic Functions
9.3 Graphing Quadratic Functions
9.3 Graphing Quadratic Equations
If an equation is in standard form, complete
the square first to get vertex form in order to
graph.
Graph the equation:
y = x2 - 4x + 5
The graph opens _____ and the vertex is a ___.
The graph is _________ than the graph of y = x2.
The axis of symmetry is ______.
Graph the equation:
y = -2(x - 4)2 + 9
The graph opens _____ and the vertex is a ___.
The graph is _________ than the graph of y = x2.
The axis of symmetry is ______.
9.3 Graphing Quadratic Functions
9.3 Graphing Quadratic Equations
If an equation is in standard form, complete
the square first to get vertex form in order to
graph.
Graph the equation:
y = -x2 - 2x + 8
The graph opens _____ and the vertex is a ___.
The graph is _________ than the graph of y = x2.
The axis of symmetry is ______.
Graph the equation:
y = 2x2 + 12x + 10
The graph opens _____ and the vertex is a ___.
The graph is _________ than the graph of y = x2.
The axis of symmetry is ______.
9.3 Graphing Quadratic Functions
9.3 Graphing Quadratic Equations
Use the following graphs to identify the
features of the quadratic function.
a. State the minimum/maximum value and label it as a max/min.
b. Give the equation for the axis of symmetry.
c. State the domain of the function.
d. State the range of the function.
1.
a.
b.
c.
d.
3.
a.
b.
c.
d.
2.
a.
b.
c.
d.
4.
a.
b.
c.
d.