TASC Math Exam: Graphing a Quadratic in the Standard Form

By Stuart Donnelly

If you’re given the standard form of a quadratic equation on the TASC Math exam, the equation provides valuable information when you’re asked to graph it.

A quadratic function is a polynomial in which the highest degree is two. The shape of the graph representing the quadratic function is called a parabola, which is a U shape.

You can create a table, select values for the independent variable (x), and substitute in and solve for the values of the dependent variable (y). Similar to how it takes two points to construct a line, you need a minimum of three points to make a parabola.

The standard form of a quadratic function is y = ax2 + bx + c.

To graph a quadratic function in standard form, follow these steps:

  1. Determine the axis of symmetry
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    (this is also the x-coordinate of the vertex).
  2. Substitute the value obtained in Step 1 back into the original formula to determine the y-coordinate of the vertex.
  3. Pick two points that are equidistant from the x-coordinate of the vertex.
  4. Substitute these values into the original formula (these resulting y-coordinates should be the same if the x-coordinates are the same distance away).
    Try to pick when x = 0 as one of the values because doing so simplifies the algebra.
  5. Plot the three points (vertex and two points from Step 4) on the coordinate plane.
  6. Connect the points you plotted in a smooth curve (careful, you don’t want to make the graph pointy or V-shaped).

Here’s an example:

y = 2x2 – 4x + 3

a = 2 b = –4 c = 3

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y coordinate:

y = 2(1)2 – 4(1) + 3

y = 2(1) – 4 + 3

y = 1

vertex: (1, 1)

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Because 0 is one away from 1, you pick 2 as the other point. To obtain the y-values, substitute 0 and 2 back into y = 2x2 – 4x + 3 and solve.

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