Findtheminimumvalueoftheparabolay = x2 + 5x.Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Question
Findtheminimumvalueoftheparabolay = x2 + 5x.Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Solution
To find the minimum value of the parabola y = x^2 + 5x, we first need to complete the square.
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The general form of a parabola is y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola.
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To rewrite the equation y = x^2 + 5x in this form, we need to add and subtract (5/2)^2 inside the square.
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So, y = (x^2 + 5x + (5/2)^2) - (5/2)^2 = (x + 5/2)^2 - (5/2)^2.
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Now, the equation is in the form y = a(x-h)^2 + k, where h = -5/2 and k = -(5/2)^2.
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The minimum value of the parabola is the y-coordinate of the vertex, which is k = -(5/2)^2 = -6.25.
So, the minimum value of the parabola y = x^2 + 5x is -6.25.
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