Q&A for How to Graph a Parabola

Draw a smooth line through the points you've graphed. Keep in mind the U-shape of the parabola. Put arrows at the ends.

This is no different from any other parabola. Make a two-column table. Choose convenient values for x. Calculate the corresponding values for y or f(x). Plot the paired-value points on a grid. Connect the points.

It's not possible simply to view a parabola and deduce its equation. If a parabola is "given," that implies that its equation is provided.

The axis of symmetry doesn't need to be 0 for you to make a table. To make a table, simply choose a value for x, such as 0, and plug it into the original equation to solve for y. Record the value of y, and that gives you a point to use when graphing the parabola.

To widen the parabola, simply modify the value of “a”, as this has an influence on the width of the parabola. I believe “b”, which can influence the axis of symmetry, also interacts with intensity. This is because they are multiplied with “x” to provide a larger or smaller value to “y”, and this is also why it can curve up or down depending on the positivity of the “a” coefficient.