JAMB - Mathematics (1983 - No. 40)

Which of the following equations represents the graph?

y = 1 + 2x + 3x2
y = 1 - 2x + 3x2
y = 1 + 2x - 3x2
y = 1 - 2x - 3x2
y = 3x2 + 2x - 1

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 \(\frac{1}{3}\) = -\(\frac{1}{3}\)

\(x^2\) - (sum of roots)x + (product of roots) = 0

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

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

3\(x^2\) + 2x - 1 = 0( multiple through by -1 since the graph of the quadratic equation is maximum)

1 - 2x - 3\(x^2\).

 

 

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