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How to Make a Parabola Pass Through a Point

Mathematical functions allow for the manipulation of a set of inputs in order to create an output. There are many different types of mathematics functions including quadratics, exponential and power functions. Quadratic functions are those that involve terms to the power of 2, and when graphed they have a parabolic dependence. All mathematical functions can be translated to ensure that they pass through a given point. This can be achieved by a simple manipulation of the function.

Things You'll Need

Graph paper

Instructions

- 1
  Write down the equation for the parabola. The simplest functional form of a parabola is: y=x^2.
  
  The graph of this function passes through the origin (0,0) point.
- 2
  Write down the equation of the translated function. For example, if the parabola needs to pass through the point (a,b), then the translated function is: y=(x-a)^2 + b
  
  A specific example is when the parabola needs to pass through the point (4,4). The translated equation then becomes: y=(x-4)^2 + 4
- 3
  Plot the graph. Draw the graph axes. Following the example, label the x-axis "x" and the y-axis "y=(x-4)^2 + 4". Plot points for a range of x values. The graph should pass through the point (4,4).

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