A quadratic function is one that relates a dependent variable to the square (2nd power) of the independent variable.

Quadratic functions can be represented in four different ways:

1. verbal description
2. graph
3. table of values
4. equation.

Each of these representations gives us information about the function and the relationship between two variables.

Verbal Description

“The quadratic parent function has a minimum (vertex) at the origin, has one x-intercept at (0,0), and its line of symmetry is the y-axis (x = 0).”

The quadratic parent function is represented below in three ways.

• Study the relationship between the points on the graph and the table of x and y values.
• The graph of the quadratic function has several critical attributes that are also evident from the table. Those attributes are a vertex (maximum or minimum point), y-intercept. x-intercepts, also called zeros, and a vertical line of symmetry.
• For the parent function shown above, the following are the critical attributes:

Can you identify the coordinates of the vertex and intercepts and the equation of the line of symmetry?

vertex Interactive button. Assistance may be required. __________ (0,0)

y-intercept Interactive button. Assistance may be required. __________ (0,0)

x-intercept Interactive button. Assistance may be required. __________ (0,0)

(vertical) line of symmetry Interactive button. Assistance may be required. __________ x = 0 (y-axis)

Every point on the graph of a quadratic function except the vertex has a point that is symmetric to it (reflected across the line of symmetry). Pairs of symmetric points will have the same y-values. Notice the points designated and shown on the table:

Use your graphing calculator to investigate by scrolling up and down the table of values to see the infinite number of symmetric points.

Interactive popup. Assistance may be required. Click here for calculator help.

Calculator Help

Go to Y= and enter x².

Press 2nd then Graph to see the table.

(If you want to begin your exploration at the same place on your table as you see above, press 2nd, then Window to set the starting x value for your table. Choose 1 for ΔTbl to get the same increments as above)

For additional calculator help see the resource section.