This week in math we learned how to determine the properties of a quadratic function. On a graph, a quadratic function looks like a U or upside down U, it’s possible it could be a V as well. This is called a parabola shape, which means it’s symmetrical. The information we want to find out about a quadratic function is the vertex, the line of symmetry, x and y-intercept, and domain and range. Some of these words we learned newly, such as vertex and line of symmetry. Vertex is the very bottom or top point of the parabola, a vertex can either be minimum (lowest point) or maximum (highest point). The line of symmetry is the invisible line that runs directly down the middle of the parabola.
As a refresher, the x-intercept is where the line(s) cross the x axis and the y-intercept the same, but for the y-axis. When finding these for a quadratic function, they will ideally be listed in the (x,y) format. Remember, you can use the three different equations we previously to find the x-axis if needed (factoring, completing the square, quadratic formula) Domain is the x-axis, so side to side. Range is the y-axis, so up and down. You can figure these out by looking at the graph, remember these deal with inequalities.
When trying to figure out if a function is quadratic by looking at only a table of values, know that it’s linear if the y values have the same different throughout. If it’s quadratic, the second set of differences (find differences of y values, then differences of differences) will be the same.
Now we put this all together: example below of a solved question.