Write the equation of the parabola that passes through the points (–3,24), (–2,0), 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.
Question
Write the equation of the parabola that passes through the points (–3,24), (–2,0), 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.
Solution
To find the equation of the parabola that passes through the points (-3,24), (-2,0), and (3,0), we can use the form y=a(x–p)(x–q), where a, p, and q are the x-intercepts of the parabola.
From the points given, we can see that the x-intercepts are -2 and 3. Therefore, p = -2 and q = 3.
So, the equation of the parabola is y = a(x - (-2))(x - 3) = a(x + 2)(x - 3).
To find the value of a, we can use the third point (-3,24). Substituting x = -3 and y = 24 into the equation, we get:
24 = a(-3 + 2)(-3 - 3) 24 = a(-1)(-6) 24 = 6a a = 24 / 6 a = 4
So, the equation of the parabola that passes through the points (-3,24), (-2,0), and (3,0) is y = 4(x + 2)(x - 3).
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