# TASC Math Exam: Graphing a Quadratic in the Standard Form

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* =* ax ^{2}* +

*bx*+

*c*.

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

- Determine the axis of symmetry

(this is also the*x*-coordinate of the vertex). - Substitute the value obtained in Step 1 back into the original formula to determine the
*y*-coordinate of the vertex. - Pick two points that are equidistant from the
*x*-coordinate of the vertex. - 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. - Plot the three points (vertex and two points from Step 4) on the coordinate plane.
- 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* = 2*x*^{2} – 4*x* + 3

*a* = 2 *b* = –4 *c* = 3

*y* coordinate:

*y* = 2(1)^{2} – 4(1) + 3

*y* = 2(1) – 4 + 3

*y* = 1

vertex: (1, 1)

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* = 2*x*^{2} – 4*x* + 3 and solve.