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
    (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


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 = 2x2 – 4x + 3 and solve.


About This Article

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About the book authors:

Stuart Donnelly, PhD, earned his doctorate in mathematics from Oxford University at the age of 25. Since then, he has established successful tutoring services in both Hong Kong and the United States and is considered by leading educators to be one of the most experienced and qualified private tutors in the country. Nicole Hersey, PhD, is a lecturer at the University of Rhode Island, with a dual appointment to the School of Education and the Department of Mathematics. Ron Olson, MA, is an NBCT-certified teacher in Social Studies who teaches AP Government, Civics, and Contemporary World Problems at Clover Park High School in Lakewood, WA. In addition to his 35 years of teaching experience, he works as an AP US History workshop consultant for The College Board and has been the advisor for National Honor Society at his high school. Shannon Reed, MA, MFA, is a visiting lecturer at the University of Pittsburgh, where she teaches composition, creative writing, and business writing.

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