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

Maths

Checking and securing understanding of drawing quadratic graphs

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

Advanced problem solving with non-linear graphs

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

$$x=-2$$ and $$x=3$$ are __________ of the equation shown in this graph.

(3, 1) is the __________ of this quadratic graph.

$$(x-3)(x-4)$$, therefore roots at $$x=3$$ and $$x=4$$

$$(x+6)(x-2)$$, therefore roots at $$x=-6$$ and $$x=2$$

$$(x-6)(x+2)$$, therefore roots at $$x=6$$ and $$x=-2$$

$$(x+3)(x+4)$$, therefore roots at $$x=-3$$ and $$x=-4$$

Factorise $$y=x^2-4x-12$$ to find the roots of the equation.

The quadratic equation $$y=x^2+14x+49$$ has __________.

What shape is the graph of the equation $$y = 6x^2-3x+9$$?

What is the $$y$$-intercept of this linear graph?

Which of these are key features of the graph of the equation $$3x+y=6$$?

Key features of a quadratic graph

Lesson outcome