Questions: Which of the following functions best describes this graph? A. y=x^2+7x+10 B. y=x^2+5x+12 C. y=(x-2)(x-5) D. y=(x+5)(x-3)

Which of the following functions best describes this graph? A. y=x^2+7x+10 B. y=x^2+5x+12 C. y=(x-2)(x-5) D. y=(x+5)(x-3)
Transcript text: Which of the following functions best describes this graph? A. $y=x^{2}+7 x+10$ B. $y=x^{2}+5 x+12$ C. $y=(x-2)(x-5)$ D. $y=(x+5)(x-3)$
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Solution

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Solution Steps

Step 1: Find the x-intercepts

The graph intersects the x-axis at x = -5 and x = 2. These are the roots of the quadratic equation.

Step 2: Determine the equation in factored form

Since the roots are x = -5 and x = 2, the factored form of the quadratic equation is y = (x + 5)(x − 2) or y = (x - 2)(x + 5). Note: The order of the factors does not matter.

Step 3: Check if the provided answer choices match

Option C is y = (x − 2)(x − 5). Option D is y = (x + 5)(x − 3). Neither match exactly. Expand option D to get y= x² + 5x -3x -15 = x² +2x - 15 which also does not fit the graph.

Option A: y = x² + 7x + 10 factors into y=(x+5)(x+2) Option B: y = x² + 5x + 12 does not easily factor.

Only option C has the correct factors albeit with the incorrect signs for the second factor.

Final Answer: The correct answer is C. y = (x - 2)(x - 5). The question or the graph has issues as the visible roots in the graph are x=2 and x=-5, but none of the answer choices match this graph exactly.

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