Question

which polynomial function could be represented by the graph below?

\\(f(x) = x^2 + x - 2\\)
\\(f(x) = 2x^2 + 2x - 4\\)
\\(f(x) = x^2 - x - 2\\)
\\(f(x) = 2x^2 - 2x - 4\\)

Explanation:

Identify the roots from the graph

Using the Polynomial Roots knowledge point

$$ x = -2, \quad x = 1 $$

Determine the factored form

Using the Polynomial Functions knowledge point

$$ f(x) = a(x + 2)(x - 1) = a(x^2 + x - 2) $$

Use the y-intercept to find the leading coefficient

Using the Polynomial Functions knowledge point

$$
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$$

Expand to standard form

Using the Polynomial Functions knowledge point

$$ f(x) = 2(x^2 + x - 2) = 2x^2 + 2x - 4 $$

Answer:

• (A) \(f(x) = x^2 + x - 2\)
• (B) \(f(x) = 2x^2 + 2x - 4\) (Correct answer)
• (C) \(f(x) = x^2 - x - 2\)
• (D) \(f(x) = 2x^2 - 2x - 4\)