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find the y cordinate of the function f(x)=x^2-4x+3

Algebra
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f(x)=x^2-4x+3.Find the y-coordinate and state the vertex as an ordered pair.

Graph the function

Apr 28th, 2015

For a quadratic function f(x) = ax^2 + bx + c the x-coordinate of the vertex equals x = -b/(2a) = -(-4)/(2*1) = 2

The y-coordinate of the vertex is y(2) = 2^2 - 4*2 + 3 = 4 - 8 + 3 = -1. Thus, the vertex is the point (2, -1). Note that a = 1 > 0 and the vertex presents a minimum of the function. 

To graph the function we may find some additional information about it. The y-intercept is y(0)= 3 and the x-intercepts can be found after we factor the function: (x - 1)(x - 3) = 0, that is, x = 1 and x = 3. Note that y > 0 for x > 3 and x < 1, whereas y < 0 if 1 < x < 3. The graph is presented below.


Apr 28th, 2015

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