Using graphs to solve equationsAQA A-Level Maths: Mind map

Exam questions on Using graphs to solve equations

1. A student draws the curve $y=x^2-4x-5$ and the straight line $y=2x-5$ on the same axes.
   The student now wants to solve $x^2-4x-3=0$ using the same curve. Find the equation of the straight line that should be drawn.2 marks
2. The graph of $y=x^3-3x$ is drawn, with a horizontal line $y=k$ on the same axes. The curve has a maximum at $(-1,2)$ and a minimum at $(1,-2)$.
   State the values of $k$ for which the equation $x^3-3x=k$ has exactly one real solution.2 marks
3. A curve has equation $y=x^2-5x+2$ and a line has equation $y=x-7$.
   Show that the $x$-coordinates of any points where the line meets the curve satisfy $x^2-6x+9=0$, and explain what this tells you about the line.3 marks