The table represents a <em>quadratic</em> function if and only if f(h - d) = f(h + d), where d is the distance of the x-value with respect to the x-coordinate of the vertex of the parabola, represented by the variable h.
<h3>How to determine that a table represents a quadratic function</h3>
<em>Quadratic</em> functions are polynomials of the form y = a · x² + b · x + c, which can be rewritten on <em>vertex</em> form: y - k = a · (x - h)², where (h, k) is the vertex of the function. Graphically speaking, <em>quadratic</em> functions are parabolae.
The axis of symmetry passes through the function and therefore we can infer that the table given represents a <em>quadratic</em> function if and only if the following condition is met:
f(h - d) = f(h + d) (1)
Where d is the distance of the x-value with respect to the x-coordinate of the vertex of the parabola, represented by the variable h. If all possible pairs observes (1), then we are in front of a <em>quadratic</em> equation.
To learn more on quadratic equations: brainly.com/question/1863222
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