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Intercept Form of a Quadratic Function
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# Factored Form of a Quadratic Function

A quadratic function is said to be written in factored form or intercept form if it follows a specific format.

y=a(xp)(xq)

Here, a, p, and q are real numbers with a0. The value of a gives the direction of the parabola. When a>0, the parabola faces upward, and when a<0, it faces downward. The zeros of the parabola are p and q, and the axis of symmetry is the vertical line with equation

## Example

Consider the graph of Comparing the generic factored form with the example function, the values of a, p, and q can be identified.
These values determine the characteristics of the parabola that can be seen in the graph.
Direction Zeros Axis of Symmetry
p=7 and q=13

Since is greater than 0, the parabola opens upward. The zeros are 7 and 13. Therefore, the parabola intersects the x-axis at (7,0) and (13,0). The axis of symmetry is the vertical line x=10.