Math Algebra grade 11

Question

A student was exploring the properties of the graphs of quadratic functions.

They plotted the family of curves y = -2 (x - 4)² + q  for various values of q

In order for the graph to have one x- intercept, the value of q must be....

Answer 1

In order for a quadratic function (graph is a parabola) to have exactly one x-intercept, the vertex must lie on the x-axis. Otherwise the graph will have two x-intercepts or zero x-intercepts.

The given function definition is written in vertex form. The x coordinate of the vertex is 4. The y coordinate in the given form is q. In order for the vertex to lie on the x-axis q must equal 0.

Visit the following Desmos graph, slide the vertex to various positions to see that the only time there is one x-intercept is when q = 0. Click the "Set" link to set q to zero.

desmos.com/calculator/hz1yrb0wih