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Find analytical expression from graph

Question:

The vertex of the quadratic function is (3, -2) and it passes the point (2, -5). Find the analytical expression of the quadratic function.

how to find analyical expression of a quadratic function from its graph?

Solution:

The vertex form of a quadratic function is: y = a (x - h)2 + k, in which h is the x-coordinate of the vertex and k is the y-coordinate of the vertex. We are given the vertex coordinate is (3, -2). So, h = 3 and k = -2. Therefore, the quadratic function of the graph is y = a (x - 3)2 - 2. Because the point (2, -5) lies on the graph, so, the point (2, -5) satisfy the quadratic function. Substitute (2, -5) into the quadratic function,

-5 = a (2 - 3)2 - 2
-5 = a (-1)2 - 2
-5 = a - 2
-5 + 2 = a
a = -3

Therefore, the quadratic function is y = -3 (x - 3)2 - 2. Watch the video for more details.