The function that would match the graph is expressed as x² + 6x + 6.75
The curve on the given graph is a quadratic graph.
The point where the curve cuts the x-axis are the zeros of the equation:
From the given graph, we can see that the curve intersect the x-axis at x = -1.5 and -4.5
The factors of the equations will be (x+1.5) and (x + 4.5)
Take the product of the factors to get the required function:
P(x) = (x+1.5)(x+4.5)
P(x) = x² + 4.5x + 1.5x + 6.75
P(x) = x² + 6x + 6.75
Hence the function that would match the graph is expressed as x² + 6x + 6.75
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