Write the equation of the parabola that passes through the points (–5,28), (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 (–5,28), (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 (-5,28), (2,0), and (3,0), we can use the fact that the equation of a parabola in the form y=a(x–p)(x–q) will pass through the points (p,0) and (q,0).
From the given points, we can see that p=2 and q=3.
So, the equation of the parabola is y=a(x-2)(x-3).
To find the value of 'a', we can use the third point (-5,28).
Substitute x=-5 and y=28 into the equation:
28=a(-5-2)(-5-3)
28=a(-7)(-8)
28=a*56
Solving for 'a' gives a=28/56=0.5.
So, the equation of the parabola that passes through the points (-5,28), (2,0), and (3,0) is y=0.5(x-2)(x-3).
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