A quadratic is an equation, graph, or sequence whereby the highest exponent of the variable is 2 The general form for a quadratic is $$ax2 + bx + c$$

A parabola is a curve where any point on the curve is an equal distance from a fixed point (the focus), and a fixed straight line (the directrix).

Checking and securing understanding of drawing quadratic graphs

Maths

In this unit, pupils consider other types of graphs. In the future unit, pupils consider different types of sequences such as Fibonacci and oscillating. Their knowledge is consolidated by linking all prior learning together.

In the prior unit, pupils studied the graphical representation of a geometric sequence and linked features of the graph to its equation. In this unit, other types of graphs are introduced and their key features identified.

Non-linear graphs

When drawing the graph of an equation, the roots of the equation are where its graph intercepts the x-axis (where y = 0).

The turning point of a graph is a point on the curve where, as x increases, the y values change from decreasing to increasing or vice versa.

Key features of a quadratic graph

A cubic is an equation, graph, or sequence whereby the highest exponent of the variable is 3

Drawing cubic graphs

Key features of a cubic graph

The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1

Drawing reciprocal graphs

An asymptote is a line that a curve approaches but never touches.

Key features of a reciprocal graph

The general form for an exponential equation is $$y = ab^x$$ where $$a$$ is the coefficient, $$b$$ is the base and $$x$$ is the exponent.

Drawing exponential graphs

The general form for an exponential equation is y = ab^x where a is the coefficient, b is the base and x is the exponent.

Key features of an exponential graph

The radius is any line segment that joins the centre of a circle to its edge.

Drawing the graph for the equation of a circle

A quadratic is an equation, graph, or sequence whereby the highest exponent of the variable is 2

Non-linear graphs

Choose a lesson (10)

Some of these lessons will soon be taken down.