Sketch then solve related equations

Questions that ask to sketch the curve and then solve equations involving transformations of the function or intersections with other curves/lines.

2 questions · Standard +0.6

Sort by: Default | Easiest first | Hardest first

Sketch the graph of $y = x(x - 3)^2$. [3]
Show that the equation $x(x - 3)^2 = 2$ can be expressed as $x^3 - 6x^2 + 9x - 2 = 0$. [2]
Show that $x = 2$ is one root of this equation and find the other two roots, expressing your answers in surd form. Show the location of these roots on your sketch graph in part (i). [8]

On separate diagrams sketch the curves with the following equations. On each sketch you should mark the coordinates of the points where the curve crosses the coordinate axes.
1. $y = x^2 - 2x - 3$
2. $y = x^2 - 2|x| - 3$
3. $y = x^2 - x - |x| - 3$
[7]
Solve the equation $$x^2 - x - |x| - 3 = x + |x|$$ [4]