Write the equation of the parabola that passes through the points (3,0), (5,0), and (6,–12).Write 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 (3,0), (5,0), and (6,–12).Write 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 (3,0), (5,0), and (6,-12).
Since the y-values of the points (3,0) and (5,0) are zero, we know that 3 and 5 are the roots of the parabola. Therefore, the equation of the parabola can be written in the form y = a(x - 3)(x - 5).
To find the value of 'a', we can substitute the x and y values of the third point (6,-12) into the equation:
-12 = a(6 - 3)(6 - 5) -12 = a(3)(1) -12 = 3a a = -12 / 3 a = -4
Therefore, the equation of the parabola that passes through the points (3,0), (5,0), and (6,-12) is y = -4(x - 3)(x - 5).
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