To find the equation of the parabola that passes through the points (-4,0), (3,0), and (-1,-6), we can use the fact that the x-coordinates of the points where the parabola crosses the x-axis (the roots of the equation) are the values of p and q in the equation y=a(x–p)(x–q).

From the given points, we can see that the parabola crosses the x-axis at x=-4 and x=3. So, p and q are -4 and 3.

The equation of the parabola is then in the form y=a(x–(-4))(x–3) = a(x+4)(x-3).

To find the value of a, we can use the third point (-1,-6) which lies on the parabola. Substituting x=-1 and y=-6 into the equation gives:

-6 = a(-1+4)(-1-3)
-6 = a(3)(-4)
-6 = -12a

Solving for a gives a = -6 / -12 = 0.5.

So, the equation of the parabola is y=0.5(x+4)(x-3).

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To find the equation of the parabola that passes through the points (-4,0), (3,0), and (-1,-6), we can use the fact that the x-coordinates of the points where the parabola crosses the x-axis (the roots of the equation) are the values of p and q in the equation y=a(x–p)(x–q).

From the given points, we can see that the parabola crosses the x-axis at x=-4 and x=3. So, p and q are -4 and 3.

The equation of the parabola is then in the form y=a(x–(-4))(x–3) = a(x+4)(x-3).

To find the value of a, we can use the third point (-1,-6) which lies on the parabola. Substituting x=-1 and y=-6 into the equation gives:

-6 = a(-1+4)(-1-3)
-6 = a(3)(-4)
-6 = -12a

Solving for a gives a = -6 / -12 = 0.5.

So, the equation of the parabola is y=0.5(x+4)(x-3).

Knowee AI · Accepted Answer

To find the equation of the parabola that passes through the points (-4,0), (3,0), and (-1,-6), we can use the fact that the x-coordinates of the points where the parabola crosses the x-axis (the roots of the equation) are the values of p and q in the equation y=a(x–p)(x–q).

From the given points, we can see that the parabola crosses the x-axis at x=-4 and x=3. So, p and q are -4 and 3.

The equation of the parabola is then in the form y=a(x–(-4))(x–3) = a(x+4)(x-3).

To find the value of a, we can use the third point (-1,-6) which lies on the parabola. Substituting x=-1 and y=-6 into the equation gives:

-6 = a(-1+4)(-1-3)
-6 = a(3)(-4)
-6 = -12a

Solving for a gives a = -6 / -12 = 0.5.

So, the equation of the parabola is y=0.5(x+4)(x-3).

Write the equation of the parabola that passes through the points (–4,0), (3,0), and (–1,–6).Write your answer in the form y=a(x–p)(x–q), where a, p, and q are integers, decimals, or simplified fractions.

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