PARABOLAS
A parabola is a graph of a quadratic.
The graph of y = x2 is shown.
This graph has a minimum turning point at (o,o).
We can sketch the graph of y = ax2 + bx + c by:
• constructing a table of values to find points on the graph
• finding the key points: the roots, y-intercept and turning point.
Axis of Symmetry
All parabolas have a vertical line of symmetry through the turning point.
The equation of the line of symmetry for the graph above is x = 0.
y-intercept
The y-intercept is the point where the parabola crosses the y-axis. We can find the y-intercept
by letting x = 0.
Roots
The roots of the parabola are the point where it crosses the x-axis. To find the roots we let
y = 0 and solve the quadratic equation. (See notes on quadratic equations)
Turning Point
2
The graph of y = ax + bx + c will have a minimum turning point when a > 0 and a maximum
turning point when a < 0.
We can find the turning point if we know the roots, the x coordinate of the turning point is half
way between the roots. To find the y coordinate substitute the x coordinate into the equation.
We can also find the turning point by completing the square. (See completing the square
notes)
Parabola Practice
http://www.bbc.co.uk/education/guides/zs9wxnb/revision/1
http://www.supermathsworld.com/ - Ask your teacher for the login details.
From the home page select Expert, select Quadratics, select Quadratic 1 Graph Sketching.
http://www.mathsisfun.com/geometry/parabola.html