The quadratic function representing the given graph is y = x² + 7x + 10. Hence, option B is the right choice.
How is the graph of a quadratic function related to its roots?
The root of any function is the x-coordinate of the point where the graph of the function intersects the x-axis.
A quadratic function has two roots.
If we suppose the roots of a quadratic function to be α and β, that is, if we assume the quadratic function to intersect the x-axis at points (α, 0) and (β, 0), then the equation of the quadratic function can be written as y = (x - α)(x - β).
How to solve the question?
In the question, we are asked to find the function represented by the given graph.
As the graph intersects the x-axis at the points (-2, 0) and (-5, 0), -2 and -5 are the roots of the given quadratic function.
Thus, we can write the equation as:
y = (x - (-2))(x - (-5)) {Since, when the roots of a quadratic function are α and β, then its equation is y = (x - α)(x - β)}.
To find the exact quadratic function, we simplify the above equation:
y = (x + 2)(x + 5),
or, y = x² + 2x + 5x + 10 {Expanding the equation},
or, y = x² + 7x + 10.
Thus, the quadratic function representing the given graph is y = x² + 7x + 10. Hence, option B is the right choice.
Learn more about quadratic functions at
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