What will the graph of y=x^2 - 2x

Name: Bryony
Who is asking: Student
Level of the question: Elementary

Question: what will the graph of y=x² - 2x - 3 be?

thanks

Hi Bryony.

y = x² - 2x - 3 is a parabola. Since the x² is positive, it opens upward (concave-up). If you factor the right hand side, you get (x+1) (x-3) so that means that the
x-intercepts are at -1 and +3. The vertex is halfway between these of course
(at x = 1). That means the vertex is at x = 1 and y = 1² - 2(1) - 3 = -4.

So draw a parabola shape with the vertex at (1, -4) and x intercepts at -1 and +3.

Hope this helps,
Stephen La Rocque.