#4.2
Understand how to find intersection points of a curve with coordinate axes.
Including relating this to the solution of an equation.
#4.3
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 \(x = -p\).
#4.4
Be able to sketch and interpret the graphs of simple functions including polynomials.
Including cases of repeated roots for polynomials.
#4.5
Be able to use stationary points when curve sketching.
Including distinguishing between maximum and minimum turning points.
#4.6
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.
#4.7
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.
#4.8
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.
\(\begin{pmatrix} a \\ b \end{pmatrix}\), \(a\bold{i} + b\bold{j}\)