Question
Determine the quadratic function f whose graph is given. The vertex is (2, -1) and the other given point is (1, 2)
Determine the quadratic function f whose graph is given. The vertex is (2, -1) and the other given point is (1, 2)
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Koala Tutor
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The general form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.
Given that the vertex is (2, -1), we can substitute h = 2 and k = -1 into the equation to get f(x) = a(x - 2)² - 1.
We also know that the point (1, 2) lies on the graph of the function, so we can substitute x = 1 and f(x) = 2 into the equation to solve for a:
2 = a(1 - 2)² - 1
2 = a(1) - 1
2 + 1 = a
a = 3
So, the quadratic function is f(x) = 3(x - 2)² - 1.
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