A-Level Maths OCR B (MEI) H640

Understand and use graphs of functions.

Understand how to find intersection points of a curve with coordinate axes.

Including relating this to the solution of an equation.

Understand and be able to use the method of completing the square to find the line of symmetry and turning point of the graph of a quadratic function and to sketch a quadratic curve (parabola).

• The curve $y = a(x + p)^2 + q$ has
• a minimum at $(-p, q)$ for $a > 0$ or a maximum at $(-p, q)$ for $a < 0$
• a line of symmetry $x = -p$.

Be able to sketch and interpret the graphs of simple functions including polynomials.

Including cases of repeated roots for polynomials.

Be able to use stationary points when curve sketching.

Including distinguishing between maximum and minimum turning points.

Be able to sketch and interpret the graphs of $y = \dfrac{a}{x}$ and $y = \dfrac{a}{x^2}$.

Including their vertical and horizontal asymptotes and recognising them as graphs of proportional relationships.

Be able to sketch curves of the forms $y = af(x)$, $y = f(x) + a$, $y = f(x + a)$ and $y = f(ax)$, given the curve of $y = f(x)$ and describe the associated transformations.

Be able to form the equation of a graph following a single transformation.

Including working with sketches of graphs where functions are not defined algebraically.

Notation:

• Map(s) onto.
• Translation, stretch, reflection.

Understand the effect of combined transformations on a graph and be able to form the equation of the new graph and to sketch it.

Be able to recognise the transformations that have been applied to a graph from the graph or its equation.

Notation:

• Vector notation may be used for a translation.
• $\begin{pmatrix} a \\ b \end{pmatrix}$, $a\bold{i} + b\bold{j}$

Be able to use stationary points of inflection when curve sketching.