You will find the equation of a parabola when two or three of its points are given.
After completing this tutorial, you will be able to complete the following:
A quadratic function can be written in one of the following forms:
· General Form: f(x) = ax2 + bx + c, where a, b and c are real numbers and a ? 0.
· Intercept form: f(x) = a(x - p)(x - q), where a ? 0 and p and q are the x-intercepts or zeros of a quadratic function.
· Vertex Form: f(x) = a(x - h)2 + k, where a ? 0 and (h, k) is the vertex of a quadratic function.
Depending on what information we have, we use one of the forms to find the equation of the parabola. The information we have will tell us the appropriate method for reaching the solution.
Three arbitrary points
If three arbitrary points other than the vertex or x-intercepts are given, the general form of the quadratic function is appropriate to use. Three unknowns a, b and c in the general form can only be figured out with three distinct points.
x-intercepts and one point
If the x-intercepts (or zeros) and one additional point are given, the intercept form of the quadratic function is appropriate to use. We can also use the general form of the function, since we have 3 distinct points and we can figure out the unknowns a, b and c in the general form with the given points. But using the intercept form and calculating the unknowns p, q and a is much more effective method in this case.
Vertex and one point
If the vertex and one additional point are given, the vertex form of the quadratic function is appropriate to use. Note that this is the only form we can use to find the equation of the parabola, since we have only two distinct points.
|Approximate Time||45 Minutes|
|Pre-requisite Concepts||Learners should be familiar with the general form of a quadratic function, intercept form of a quadratic function, parabola, quadratic function, vertex , vertex form of quadratic function, and x-intercept.|
|Type of Tutorial||Procedural Development|
|Key Vocabulary||general form of the quadratic function, graph, intercept form of the quadratic function|