To find the equation of the parabola that passes through the points (-5,0), (-2,9), and (3,0), we can use the fact that the equation of a parabola is given by y = a(x - p)(x - q), where (p, 0) and (q, 0) are the x-intercepts of the parabola.

1. Identify the x-intercepts: From the given points, we can see that the x-intercepts are -5 and 3. So, p = -5 and q = 3.

2. Substitute the x-intercepts into the equation: This gives us y = a(x - (-5))(x - 3) = a(x + 5)(x - 3).

3. Use the third point to find 'a': The third point given is (-2,9). We can substitute these values into the equation to find 'a'. So, 9 = a(-2 + 5)(-2 - 3) = a(3)(-5) = -15a. Solving for 'a' gives a = 9 / -15 = -3/5.

So, the equation of the parabola that passes through the points (-5,0), (-2,9), and (3,0) is y = -3/5(x + 5)(x - 3).

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To find the equation of the parabola that passes through the points (-5,0), (-2,9), and (3,0), we can use the fact that the equation of a parabola is given by y = a(x - p)(x - q), where (p, 0) and (q, 0) are the x-intercepts of the parabola.

1. Identify the x-intercepts: From the given points, we can see that the x-intercepts are -5 and 3. So, p = -5 and q = 3.

2. Substitute the x-intercepts into the equation: This gives us y = a(x - (-5))(x - 3) = a(x + 5)(x - 3).

3. Use the third point to find 'a': The third point given is (-2,9). We can substitute these values into the equation to find 'a'. So, 9 = a(-2 + 5)(-2 - 3) = a(3)(-5) = -15a. Solving for 'a' gives a = 9 / -15 = -3/5.

So, the equation of the parabola that passes through the points (-5,0), (-2,9), and (3,0) is y = -3/5(x + 5)(x - 3).

Knowee AI · Accepted Answer

To find the equation of the parabola that passes through the points (-5,0), (-2,9), and (3,0), we can use the fact that the equation of a parabola is given by y = a(x - p)(x - q), where (p, 0) and (q, 0) are the x-intercepts of the parabola.

1. Identify the x-intercepts: From the given points, we can see that the x-intercepts are -5 and 3. So, p = -5 and q = 3.

2. Substitute the x-intercepts into the equation: This gives us y = a(x - (-5))(x - 3) = a(x + 5)(x - 3).

3. Use the third point to find 'a': The third point given is (-2,9). We can substitute these values into the equation to find 'a'. So, 9 = a(-2 + 5)(-2 - 3) = a(3)(-5) = -15a. Solving for 'a' gives a = 9 / -15 = -3/5.

So, the equation of the parabola that passes through the points (-5,0), (-2,9), and (3,0) is y = -3/5(x + 5)(x - 3).

Write the equation of the parabola that passes through the points (–5,0), (–2,9), and (3,0).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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