The quadratic equation to model the graph is y = x² - 6 · x + 14.
How to derive the expression of a quadratic equation from a graph
The picture presents us the graph of a parabola, whose algebraic expression is a quadratic equation. In accordance with fundamental theorem of algebra, a quadratic equation can be derived by knowing three distinct points on Cartesian plane.
If we know that (x, y) = (0, 14), (x, y) = (3, 5) and (x, y) = (6, 14), then the coefficients of the quadratic equation in standard form:
14 = c (1)
5 = 9 · a + 3 · b + c (2)
14 = 36 · a + 6 · b + c (3)
The solution of the system of linear equations is (a, b, c) = (1, - 6, 14). Hence, the quadratic equation to model the graph is y = x² - 6 · x + 14.
To learn more on quadratic equations: https://brainly.com/question/1863222
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