Write the equation of the parabola that passes through the points shown in the table.x y–2 06 07 27Write 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 06 07 27Write 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 (-2,0), (6,0), and (7,2), we can use the form y=a(x–p)(x–q), where p and q are the x-intercepts of the parabola.
From the points given, we can see that the parabola crosses the x-axis at x=-2 and x=6. Therefore, p=-2 and q=6.
We can substitute these values into the equation to get: y=a(x+2)(x-6)
To find the value of 'a', we can use the third point (7,2). Substituting x=7 and y=2 into the equation gives us: 2=a(7+2)(7-6)
Solving this equation for 'a' gives us: a=2/9
Therefore, the equation of the parabola is: y=(2/9)(x+2)(x-6)
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