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

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

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.

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

Advanced problem solving with non-linear graphs

Maths

Checking and securing understanding of drawing quadratic graphs

Key features of a quadratic graph

Drawing cubic graphs

Key features of a cubic graph

Drawing reciprocal graphs

Key features of a reciprocal graph

Drawing exponential graphs

Key features of an exponential graph

Drawing the graph for the equation of a circle

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.

In this unit graphical representations of non-linear graphs are introduced and explored, and their key features identified.

Non-linear graphs

$$y={5\over{x}}$$ would not have the axes as asymptotes.

For $$y={5\over{x}}$$ when $$x$$ is positive $$y$$ would be positive.

For $$y={5\over{x}}$$ when $$x$$ is negative $$y$$ would be negative.

This might be the graph $$y={5\over{x}}$$ 

How can you tell that this is not the graph of $$y={5\over{x}}$$?

Which of these could be the equation of this graph?

The circle $$x^2+y^2=49$$ and the line $$x+y=0$$ are drawn on the same axes. What is the area of the region bound by the circumference of the circle, the line $$x+y=0$$, and the $$y$$ axis?

__________ is a line that a curve approaches but never touches.

Laura plots the graph of $$y=x^3$$. When the $$x$$ coordinate is $$-4$$, the $$y$$ coordinate is {{ }}.  

Andeep plots the reciprocal graph $$y={1\over{x}}$$. Which of these will be coordinate pairs?

Jun graphs the circle $$x^2+y^2=16$$.  When the $$y$$ coordinate is $$3$$, the $$x$$ coordinate is {{ }}.

The general form of the equation of a circle with centre origin is $$x^2+y^2=r^2$$. What is the radius of the circle graphed by the equation $$x^2+y^2=25$$?

$$7^2-{{1\over{4}}\times{\pi}\times7^2}$$

$$7^2-{{1\over{4}}\times{\pi}\times14^2}$$

A quarter circle with radius 7 overlaps a square of length 7. Which of these calculations will give the shaded area?

Advanced problem solving with non-linear graphs

Lesson outcome