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Determine the equation of the parabola shown in the diagram in factored form.

Determine the equation of the parabola shown in the diagram in factored form.-example-1
User Messerbill
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1 Answer

2 votes

Answer:

y = (x +1)(x -3)

Explanation:

You want the equation in factored form for the parabola shown in the graph with x-intercepts at -1 and +3, and a vertical scale factor of 1.

Factors

If p is a zero (x-intercept) of the graphed polynomial function, then (x-p) is a factor. The graph shows x-intercepts at x=-1 and x=3. This means (x-(-1)) and (x -3) are factors.

Scale factor

The equation of the graph may also have a vertical scale factor. That can often be determined easily from the graph by looking at the vertical distance from the vertex of points 1 unit either side of the vertex.

Here, the vertex is (1, -4) and points at x=0 and x=2 have the value -3, which differs from the vertex by 1 unit. Hence the scale factor is 1. It multiplies the other factors.

The equation of the graphed parabola is ...

y = (x +1)(x -3)

User Bharatwaja
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