Write the equation of the parabola that passes through the points shown in the table.x y–5 –24–3 0–2 0Write your answer in the form y=a(x–p)(x–q), where a, p, and q are integers, decimals, or simplified fractions.
Question
Write the equation of the parabola that passes through the points shown in the table.x y–5 –24–3 0–2 0Write your answer in the form y=a(x–p)(x–q), where a, p, and q are integers, decimals, or simplified fractions.
Solution
The given points are (-5, -24), (-3, 0), and (-2, 0).
The general form of a parabola is y = a(x - h)² + k, but we want it in the form y = a(x - p)(x - q).
Since the y-values of the last two points are 0, we can say that p and q are -3 and -2.
So, the equation becomes y = a(x + 3)(x + 2).
To find the value of 'a', we can use the first point (-5, -24).
Substitute x = -5 and y = -24 into the equation:
-24 = a(-5 + 3)(-5 + 2)
-24 = a(-2)(-3)
-24 = 6a
So, a = -24 / 6 = -4.
Therefore, the equation of the parabola is y = -4(x + 3)(x + 2).
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