Algebra 2: Section 5-2 Properties of Parabolas
Standard: Students graph quadratic functions and determine the maxima, minima,
and zeros of the function.
Graph of a Quadratic Function in Standard Form
2
The graph of y  ax  bx  c is a parabola when a  0 .
When a > 0, the parabola opens up.
When a < 0, the parabola opens down.
b
The axis of symmetry is the line x  
2a
b
The x-coordinate of the vertex is 
2a
The y-coordinate of the vertex if the value of y obtained when you plug the xcoordinate of the vertex into the function.
The y-intercept is (0, c)
Happy
Parabola
Positive
Sad
Parabola
Negative
Quick Check
Ex. 1) a) Graph y  2 x 2  4 .
Step 1: Find and graph the vertex. x  
Note: x  
b
2a
b
is also the axis of symmetry.
2a
Step 2 : Make a table of values to find some points on both sides of the axis of
symmetry (vertex). Graph the points.
x
y
Step 3: Sketch the curve.
b) Graph y  5  3x 2 .
Step 1: Find and graph the vertex.
x
b
2a
Step 2: Find two additional points; one on each side of the vertex. x
y
Step 3: Sketch the curve.
c) What are the coordinates of the vertex of the graph of a function in the form y  ax 2 ?
x
b
2a
Day 1 Assignment page 252 #1-9 all
Section 5.2 Day 2
Quick Check
Ex. 2) Graph each function. Label the vertex and the axis of symmetry.
Find the minimum or maximum value.
1 2
2
y


x  2x  3
y


x

4
x

2
a)
b)
3
Vertex:
Vertex:
Day 2 Assignment page 252 #11-27 odds