The equation of a parabola in the form y = a(x - p)(x - q) that passes through the points (-2,0), (3,0), and (1,-48) can be found by setting up a system of equations using these points.

First, we know that the roots of the parabola are x = -2 and x = 3, because these are the x-values where y = 0. So, we can write the equation as:

y = a(x - (-2))(x - 3)

or

y = a(x + 2)(x - 3)

Next, we can use the third point (1,-48) to find the value of a. Substituting x = 1 and y = -48 into the equation gives:

-48 = a(1 + 2)(1 - 3)

or

-48 = a(3)(-2)

or

-48 = -6a

Solving for a gives a = 8.

So, the equation of the parabola is y = 8(x + 2)(x - 3).

Question

The equation of a parabola in the form y = a(x - p)(x - q) that passes through the points (-2,0), (3,0), and (1,-48) can be found by setting up a system of equations using these points.

First, we know that the roots of the parabola are x = -2 and x = 3, because these are the x-values where y = 0. So, we can write the equation as:

y = a(x - (-2))(x - 3)

or

y = a(x + 2)(x - 3)

Next, we can use the third point (1,-48) to find the value of a. Substituting x = 1 and y = -48 into the equation gives:

-48 = a(1 + 2)(1 - 3)

or

-48 = a(3)(-2)

or

-48 = -6a

Solving for a gives a = 8.

So, the equation of the parabola is y = 8(x + 2)(x - 3).

Knowee AI · Accepted Answer

The equation of a parabola in the form y = a(x - p)(x - q) that passes through the points (-2,0), (3,0), and (1,-48) can be found by setting up a system of equations using these points.

First, we know that the roots of the parabola are x = -2 and x = 3, because these are the x-values where y = 0. So, we can write the equation as:

y = a(x - (-2))(x - 3)

or

y = a(x + 2)(x - 3)

Next, we can use the third point (1,-48) to find the value of a. Substituting x = 1 and y = -48 into the equation gives:

-48 = a(1 + 2)(1 - 3)

or

-48 = a(3)(-2)

or

-48 = -6a

Solving for a gives a = 8.

So, the equation of the parabola is y = 8(x + 2)(x - 3).

Write the equation of the parabola that passes through the points (–2,0), (3,0), and (1,–48).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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