Quadratic Forming

L2MAEL

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Quadratic forming questions are almost guaranteed in the exam.
These types of questions consist of first forming a quadratic equation either in the intercept form or the vertex form, then answering the question.

The most common forms used are the vertex form and the intercept form.

VERTEX FORM: $y=a(x-p{)}^2+q$ where $(p,q)$ is the coordinates of the vertex.

INTERCEPT FORM: $y=a(x-p)(x-q)$ where $(p,0)$ and $(q,0)$ are the coordinates of the $x$-intercepts.

$a$ is the scale factor for both forms.

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Use the VERTEX FORM when:

• Can see a clear vertex coordinate

Use the INTERCEPT FORM when:

• Can see clear $x$-intercept coordinates

If you can use either, use the vertex form — it’s easier.

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e.g. If you can see a clear vertex at $(2,1)$, then the equation would be: $y=a(x-2{)}^2+1$ $a$ can be calculated by finding another coordinate that passes the graph. However, YOU CANNOT USE the same coordinate that you used. e.g. if you used the vertex form, you CANNOT USE the coordinates of the vertex to find $a$. Same applies for the intercept form.

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Once a quadratic equation is formed, answer the question appropriately!