How to Do Parabola Equations


Parabolas are the graphs of quadratic equations, or equations of the form y=ax2+bx+c. In Algebra and in many upper-level math courses, you will need to be comfortable with interpreting and graphing a parabola equation. Practice with several equations before your exam, so that you are able to carry out these interpretations smoothly!

  • Find the y-intercept of the parabola, or the point at which the parabola intersects with the y-axis, by setting the x-value in the parabola equation equal to zero. If your equation is y=x2+2x+1, setting x equal to zero gives (0,1).

  • Set the function equal to zero, to find the x-intercept. Our example becomes 0=x2+2x+1. Factoring this equation gives 0=(x+1)^2, so the x-intercept is (-1,0).

  • Find the vertex of the parabola, using the formula that the x-value of the vertex is equal to -b/2a. In our example, the vertex becomes -2/2, or -1. Plug the x-value of the vertex back into the equation, to obtain y=1-2+1, or y=0. Thus, the vertex is actually the same as the x-intercept in this example: (-1,0).

  • Determine if you have one point on either side of the vertex. Since, in this example, you only found the point on the right side of the vertex, (0,1), plug in points on the left side of the vertex so that you can start to sketch out the parabola. For instance, you could plug in x=-2 and x=-3, to find the points (-2, 1) and (-3, 4).

  • Plot your points, on a sheet of graph paper.


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