Exploring Quadratic Functions
categories: Math 11
- What is a quadratic function?
A quadratic function is a relation that can be written in standard form:
Where a is not equal to zero.
Example: - Using desmos, graph:
The sliders are at a=1, b=0, c=0 in the photo below, the graph is shown and you can see clear symmetry.
- a Now, a < 0, so I filled it in with -6.
Now the equation is
The graph now has a maximum point of zero. That’s the highest point that the graph goes to. Since the graph infinitely continues, there is no minimum point.
b. when a > 0, the graph is switched. I made a = 8. The lines on the graph now start at zero, and expand outwards toward the positive. The minimum point is zero, and there is no maximum point.
c. now -1 < a < 1. So, a is just zero. The graph is identical to the first graph, since it’s just representing the original standard form equation.
d. when a < 1, i chose -5 to be a. It looks similar to the second graph.
- By changing a into a positive, the shape of the graph opens up into the positives.
By changing a into a negative, the shape of the graph opens down into the negatives. - When changing the value of b, the shape of the graph’s symmetry changes.
- When changing the value of c, the y intercept changes.
- An equation where the curve just touches the x axis:
- An equation where you can get the roots of 1
An equation where you can get the roots of -1
- An equation where he curve does not cross the x-axis
