1. Graphing a Quadratic Equation – The Parabola
Format of a general quadratic equation:
ax2 + bx + c = 0
Format of a parabola:
y = ax2 + bx + c

2. Graphing a Quadratic Equation – The Parabola
To graph a parabola:
y = ax2 + bx + c
First, find the “Axis of Symmetry.” (AOS)
Use the formula: x = -b
2(a)
The axis of symmetry gives you the x-coordinate of the turning point.
To find the y-coordinate of the turning point, plug the x-coordinate back in to the equation
If you solved the parabola for zero, this would give you the roots of the equation

3. Graphing a Quadratic Equation – The Parabola
To graph a parabola:
Create a table – balanced around the axis of symmetry X Y
AOS Value
Y-Coordinate of Turning Point

4. Graphing a Quadratic Equation – The Parabola
Example 1: Nice and Easy
y = x2 – 4x - 5
Find the Axis of Symmetry and the Turning Point.
Try to find Roots
Complete Table
Graph Parabola X Y

5. Graphing a Quadratic Equation – The Parabola
Example 2: Downward Parabola
y = -x2 – 6x + 7
Find the Axis of Symmetry and the Turning Point
Try to find roots
Complete Table
Graph Parabola X Y

6. Graphing a Quadratic Equation – The Parabola
Example 3: When the Turning Point is NOT an Integer
y = x2 + 5x - 1
Find the Axis of Symmetry and the Turning Point
Try to find roots
Complete Table
Graph Parabola X Y

7. Graphing a Quadratic Equation – The Parabola
Example 4: When Given a Specific Interval
y = x2 – 4x + 3 (-1≤ x ≤ 5)
If given an interval, DON’T HAVE TO FIND the Axis of Symmetry and the Turning Point
Don’t need to find roots
Complete Table (x-values are given)
Graph Parabola X Y

8. Graphing a Quadratic Equation – The Parabola
Example 5: When Given the the Picture of a Parabola
Use the picture to find the roots
Work backwards from the roots to create factors.
Multiply the factors to create the parabolic equation
Make sure your equation says y =