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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

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

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