The Root of the Problem

By varying the value of the slider k, what do you notice about x-intercepts of the quadratic graph? (Hint: it will be easier to notice the pattern if you choose integer values of k)

What is the connection between the value of k and the x-intercepts of the quadratic graph?

Write the quadratic equation in factorised form using the values of the x-intercepts in terms of k. Hint: if you know the x-intercepts of a quadratic are and you can write the quadratic in factorised form as as these are the x-vales which make the quadratic zero.

Expand this equation to find the values of the coefficients b and c in terms of k

Using what you have found and without solving the quadratic. Find the value of k and hence the x-intercepts of the graph with equation.