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

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

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

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

The shape of the graph of a quadratic equation is called a {{}}.

Andeep: They will different $$y$$-intercepts.

Jacob: One parabola will be increasing, the other will be decreasing.

Sam: They will have the same shape; that of a parabola.

Some Oak pupils compare the graph of $$y=x^2$$ to the graph of $$y=x^2-6$$. Which of their statements are true?

Jun: They will have a common $$y$$-intercept.

Laura: They will have the same $$x$$-intercepts.

Sam: They have same graph because squaring a negative gives a positive result.

Sofia: One parabola will minimum $$y$$ value, the other a maximum $$y$$ value.

Some Oak pupils compare the graph of $$y=8+x^2$$ to the graph of $$y=8-x^2$$.  Which of their statements are true?

Which one of these coordinates do not satisfy the equation $$y=x^2-4x+8$$?

Use a calculator to check this table of values for the equation $$y=3x^2-7x+1$$. Identify which coordinate pair is incorrect. 

Identify the line of symmetry of the graph of the equation $$y=2x^2-6x+1$$.

$$x^2 + 5x - 7 = 0$$ is an example of a __________ equation.

In the equation $$y=x^2-5$$, what is the value of $$y$$ when $$x=4$$? {{}}

In the equation $$y=x^2-5$$, what is the value of $$y$$ when $$x=-4$$?

In the equation $$y=3-x^2$$, what is the value of $$y$$ when $$x=-2$$?

In the equation $$y=4x^2$$, what is the value of $$y$$ when $$x=-5$$? {{}}

In the equation $$y=x^2-5x-7$$, what is the value of $$y$$ when $$x=-2$$?

This lesson was made for home learning during the pandemic.

Checking and securing understanding of drawing quadratic graphs

Lesson outcome

This lesson was made for home learning during the pandemic.