Write the equation of the parabola that passes through the points shown in the table.x y–2 –12–1 06 0Write your answer in the form y=a(x–p)(x–q), where a, p, and q are integers, decimals, or simplified fractions.Submit
Question
Write the equation of the parabola that passes through the points shown in the table.x y–2 –12–1 06 0Write your answer in the form y=a(x–p)(x–q), where a, p, and q are integers, decimals, or simplified fractions.Submit
Solution
To find the equation of the parabola that passes through the points (-2, -12), (-1, 0), and (6, 0), we can use the form y = a(x - p)(x - q), where a, p, and q are constants.
First, we can identify p and q as the x-coordinates of the points where the parabola crosses the x-axis. In this case, those points are (-1, 0) and (6, 0), so p = -1 and q = 6.
Next, we can find a by substituting one of the points into the equation and solving for a. Let's use the point (-2, -12):
-12 = a(-2 - (-1))(-2 - 6) -12 = a(-1)(-8) -12 = 8a a = -12 / 8 = -1.5
So, the equation of the parabola is y = -1.5(x + 1)(x - 6).
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