Write the equation of the parabola that passes through the points (–7,–7), (–5,0), and (–2,0).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 (–7,–7), (–5,0), and (–2,0).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 (-7,-7), (-5,0), and (-2,0), 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 -5 and -2. Therefore, p and q are -5 and -2. The equation of the parabola is then y=a(x+5)(x+2).
To find the value of a, we can use one of the points. Let's use the point (-7,-7). Substituting these values into the equation gives:
-7=a(-7+5)(-7+2) -7=a(-2)(-5) -7=a*10 a=-7/10
Therefore, the equation of the parabola that passes through the points (-7,-7), (-5,0), and (-2,0) is y=-7/10(x+5)(x+2).
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