This is a demonstration of how I anticipate using HTML, CSS, JavaScript, SVG, mathML, and mathJax to provide meaningful online instruction in basic algebra topics as found in Intermediate Algebra and College Algebra.
Problem:Analyze the quadratic function whose rule is given by
Analysis:
The function is a quadratic function so the graph is a parabola which opens up or down.
Because the leading coefficient is positive the parabola opens up.
The fact that the discriminant
is 0, implies the parabola has one x-intercept.
This same information is apparent from the fact that has only one solution. Which means the parabola has only one x-intercept.
such that it intersects the parabola in one point.
We should also observe that the x-intercept must be the vertex. Therefore the vertex and x-intercepts have the same coordinates (3,0).
The x-intercept/vertex should be marked
Because exact values cannot be inferred from a sketch it is important that we label the vertex with exact values for its coordinates.
The graph of the function is now complete.
All the important information about the function is summarized and displayed in geometic form.
Interpreting the Graph
The graph shows that the domain is all real numbers R
The graph shows that the range is all real numbers greater than or equal to 0. The range is
The graph clearly shows the answer to
and because
the answer to Where is
? is also the solution set for the equation in one variable
.
The graph clearly shows the answer to
and because
the answer to Where is
? is also the solution set for the inequality in one variable
.
The graph clearly shows the answer to
and because
the answer to Where is
? is also the solution set for the inequality in one variable
A Few Observations About the Interpretation