This week in Precalculus 11, we learned about quadratic functions and how to graph them. Quadratic functions are parabolas and they always have 2 variables (usually x and y), a degree of 2, a vertex, a line of symmetry, a domain, and a range. Both an x-intercept and a y-intercept are not mandatory but there usually at least one of them.

The Vertex is the highest or lowest point on the graph. If the parabola opens up, then the vertex is a minimum. If the parabola opens down, then the vertex is a maximum. The line of symmetry is the point where the parabola can be split in half evenly. The x-intercept is when the parabola touches the x-axis and the y-intercept is when the parabola touches the y-axis. The domain is the restrictions for the x-axis and range is the restrictions for the y-axis.

An example of a quadratic function:

y = x²+ x – 6

Since A is positive (1), we know that the parabola opens up and that the vertex is a minimum. We also know that C (-6) is the y-intercept.

To find the x-intercept roots, we have to make y = 0.

0 = x²+ x – 6

It’s now a quadratic equation, not a function, so we can solve for roots.

x²+ x – 6 = 0

(x + 3)(x – 2)

x = -3, 2

x-intercept roots: (-3, 0) and (2, 0)