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 = ax2 + 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 = 2x2 – 4x + 3
a = 2 b = –4 c = 3
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.