Intercept Form
Key points
- Another form that represents a quadratic function is intercept form, which gives the x-intercepts/zeros/solutions of the quadratic.
- f(x)=a(x-p)(x-q)
- There may be either one or two intercepts, and the equation changes accordingly.
Intercept Form is the quadratic equation form which gives the other key element of a parabola – the x-intercepts (also known as the solutions or zeros).
- Intercept form follows the structure:
- f(x)=a(x-p)(x-q)
- In this form, the intercepts are (p,0), and (q,0).
- x=p or x=q.
This form of intercept form accounts for when there are two x-intercepts. However, there may be just one x-intercept, in which the line “bounces” off the x-axis instead of crossing it.
- This is known as a “double solution/zero/root”
- Intercept form takes on the structure:
- f(x)=a(x-p)^2
- Intercept form takes on the structure:
- In this structure, the intercept is just (p,0), since there is only one intercept.
- x=p.
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