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ZingPath: Parabolas

Finding the Equation of a Parabola

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Finding the Equation of a Parabola

Algebra-1

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You will find the equation of a parabola when two or three of its points are given.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Find the equation of a parabola when its x-intercepts and an additional point are given.
  • Find the equation of a parabola when its vertex and an additional point are given.
  • Find the equation of a parabola when three arbitrary points are given.

Everything You'll Have Covered

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.

Tutorial Details

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.
Course Algebra-1
Type of Tutorial Procedural Development
Key Vocabulary general form of the quadratic function, graph, intercept form of the quadratic function