2. Parabolas
4.2

3. Standard Form of Parabolic Equations
Standard Form of Equation
Axis of Symmetry
Vertex
Direction Parabola Opens
up or down
right or left

4. Example 1
Describe the effect that each characteristic of the equation of the parabola has on its graph
The parabola opens either up or down, not left or right.
The parabola opens down and has a maximum value.
The parabola has an axis of symmetry of x = –7.
The parabola
has a vertex
of (–7, –5)

5. Example 2
Write in standard form. Identify the vertex, axis of symmetry, and direction of opening of the parabola.
Original Equation
Factor 2 from the x-terms
Complete the square on right side
The 9 added to complete the square is multiplied by 2.
Write in standard form
The vertex of this parabola is located at (3, –43)
The equations of the axis of symmetry is x = 3.
The parabola opens upward.

6. Your Turn
Write the equation in standard form. Identify the vertex, axis of symmetry, and direction of the opening.

7. Example 3 Graph The parabola opens in which direction?
Identify the vertex.
Identify the axis of symmetry.
Create a table of values with points
on either side of the vertex.
Plot the points. x y –1
4/3
7/3 1 2 3 x y –1 1 2 3