Quadratic Graphs (Cambridge International AS Mathematics)

Quadratic graphs

What are quadratic graphs?

• The general equation of a quadratic graph is $y=ax^{2}+bx+c$
• Their shape is called a parabola ("U" shape)
• Positive quadratics have a value of $a>0$ so the parabola is upright$\cup$
• Negative quadratics have a value of $a<0$ so the parabola is upside down $\cap$

How do I use quadratic graphs?

You need to be able to:

• sketch a quadratic graph given an equation or information about the graph
• determine, from the equation, the axes intercepts
• factorise, if possible, to find the roots of the quadratic function
• find the coordinates of the turning point (maximum or minimum)

You may have to rearrange the equation before you can find some of these things

Exam Hint

• Your calculator may tell you the roots of a quadratic function and the coordinates of the turning point
• But don't rely on it – think about how many marks the question is worth and how much method/working you should show
• Remember sometimes you'll need to rearrange an equation into the form $y=ax^{2}+bx+c$

Worked Example