Curve Sketching 1 (AQA A-Level Further Maths): Flashcards

$y = \frac{ax^2 + bx + c}{dx^2 + ex + f}$

Intercepts → Asymptotes → Range → Turning points

Substitute $x = 0$ into equation

Set $y = 0$, solve numerator = 0

Set denominator = 0 and solve

$y = \frac{a}{d}$ (ratio of leading coefficients)

Yes, at specific finite x-values

Rearrange as quadratic in x, apply discriminant $\geq 0$

At boundary values of the range

When numerator = 0 (and denominator $\neq 0$)