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Which of the following equations represents the graph?


Question

Which of the following equations represents the graph?

Options

A) y = 1 + 2x + 3x2

B) y = 1 - 2x + 3x2

C) y = 1 + 2x - 3x2

D) y = 1 - 2x - 3x2

E) y = 3x2 + 2x - 1

The correct answer is E.

Explanation:

The roots of the function are 1 and \(\frac{1}{3}\)

sum of roots = -1 + \(\frac{1}{3}\) = -\(\frac{2}{3}\)

product of roots = -1 x \(\frac{1}{3}\) = -\(\frac{1}{3}\)

x2 - (sum of roots)x + (product of roots) = 0

x2 + (-\(\frac{2}{3}\))x - (-\(\frac{1}{3}\)) = 0

x2 + \(\frac{2x}{3}\) - \(\frac{1}{3}\) = 0

3x2 + 2x - 1 = 0


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Dicussion (1)

  • The roots of the function are 1 and \(\frac{1}{3}\)

    sum of roots = -1 + \(\frac{1}{3}\) = -\(\frac{2}{3}\)

    product of roots = -1 x \(\frac{1}{3}\) = -\(\frac{1}{3}\)

    x2 - (sum of roots)x + (product of roots) = 0

    x2 + (-\(\frac{2}{3}\))x - (-\(\frac{1}{3}\)) = 0

    x2 + \(\frac{2x}{3}\) - \(\frac{1}{3}\) = 0

    3x2 + 2x - 1 = 0

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