The x- intercepts of a parabola are (0,-6) and (0,4). The parabola crosses the y- axis at -120. Lucas said that an equation for the parabola is y=5x^2+10x-120 and that the coordinates of the vertex are (-1, -125). Do you agree or disagree? List why?

Given:

The x- intercepts of a parabola are (0,-6) and (0,4).

The parabola crosses the y- axis at -120.

Lucas said that an equation for the parabola is and that the coordinates of the vertex are (-1, -125).

To find:

Whether Lucas is correct or not.

Solution:

The x- intercepts of a parabola are (0,-6) and (0,4). It means (x+6) and (x-4) are the factors of the equation of the parabola.

            ...(i)

The parabola crosses the y- axis at -120. It means the equation of the parabola must be true for (0,-120).

Divide both sides by -24.

Substituting in (i), we get

So, the equation of the parabola is .

The vertex of a parabola is:

In the equation of the parabola, .

Putting in the equation of the parabola, we get

So, the vertex of the parabola is at point (-1,-125).

Therefore, Lucas is correct.

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step-by-step explanation: