To find the equation of the parabola that passes through the points (-1,12), (-2,0), and (1,0), we can use the general form of a parabola equation y = a(x - h)² + k, where (h, k) is the vertex of the parabola. However, since we want the equation in the form y = a(x - p)(x - q), we need to find the roots of the parabola, which are the x-intercepts, or the points where the parabola crosses the x-axis.

From the given points, we can see that the parabola crosses the x-axis at (-2,0) and (1,0), so p and q are -2 and 1.

Now, we need to find the value of a. We can use the third point (-1,12) which lies on the parabola. Substituting these values into the equation gives:

12 = a(-1 - (-2))(-1 - 1)
12 = a(1)(-2)
12 = -2a

Solving for a gives a = -6.

So, the equation of the parabola in the form y = a(x - p)(x - q) is y = -6(x - (-2))(x - 1), or y = -6(x + 2)(x - 1).

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To find the equation of the parabola that passes through the points (-1,12), (-2,0), and (1,0), we can use the general form of a parabola equation y = a(x - h)² + k, where (h, k) is the vertex of the parabola. However, since we want the equation in the form y = a(x - p)(x - q), we need to find the roots of the parabola, which are the x-intercepts, or the points where the parabola crosses the x-axis.

From the given points, we can see that the parabola crosses the x-axis at (-2,0) and (1,0), so p and q are -2 and 1.

Now, we need to find the value of a. We can use the third point (-1,12) which lies on the parabola. Substituting these values into the equation gives:

12 = a(-1 - (-2))(-1 - 1)
12 = a(1)(-2)
12 = -2a

Solving for a gives a = -6.

So, the equation of the parabola in the form y = a(x - p)(x - q) is y = -6(x - (-2))(x - 1), or y = -6(x + 2)(x - 1).

Knowee AI · Accepted Answer

To find the equation of the parabola that passes through the points (-1,12), (-2,0), and (1,0), we can use the general form of a parabola equation y = a(x - h)² + k, where (h, k) is the vertex of the parabola. However, since we want the equation in the form y = a(x - p)(x - q), we need to find the roots of the parabola, which are the x-intercepts, or the points where the parabola crosses the x-axis.

From the given points, we can see that the parabola crosses the x-axis at (-2,0) and (1,0), so p and q are -2 and 1.

Now, we need to find the value of a. We can use the third point (-1,12) which lies on the parabola. Substituting these values into the equation gives:

12 = a(-1 - (-2))(-1 - 1)
12 = a(1)(-2)
12 = -2a

Solving for a gives a = -6.

So, the equation of the parabola in the form y = a(x - p)(x - q) is y = -6(x - (-2))(x - 1), or y = -6(x + 2)(x - 1).

Write the equation of the parabola that passes through the points (–1,12), (–2,0), and (1,0).Write your answer in the form y=a(x–p)(x–q), where a, p, and q are integers, decimals, or simplified fractions.Submit

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