In real world applications, it is important to be able to identify key features of the graph in order to determine which important part of information you are looking for.
Every parabola has the following features:
Vertex: The maximum or minimum of the parabola.
y - intercept: Where the parabola crosses the y-axis.
Axis of Symmetry: A vertical line that divides the parabola into 2 symmetric parts.
y - intercept: Where the parabola crosses the y-axis.
Axis of Symmetry: A vertical line that divides the parabola into 2 symmetric parts.
Most parabolas have:
x-intercepts: Where the parabola crosses the x-axis.
It is possible for a parabola to not touch the x-axis! Can you describe a parabola that would not touch the x-axis? There are multiple possibilities!!
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Regardless of the form of the equation, the graph will always look like a parabola:
Quadratic functions begin to change shape depending on the equation's leading coefficient!
- What if the leading coefficient was greater than 1?
- Can you predict what will happen to the graph if the leading coefficient is negative?
- What if the leading coefficient was less than 1?
Try using the Desmos website to graph the following functions and determine what the leading coefficient does to the graph: