Complete the square to rewrite y = x^2 – 6x + 5 in vertex form. then state whether the vertex is a maximum or a minimum and give its coordinates. a. minimum at (–3, –4) b. maximum at (3, –4) c. minimum at (3, –4) d. maximum at (–3, –4)

The first thing to do is to set this equal to zero, then move the constant over to the other side of the equals sign so we only have the x terms to worry about.  .  Now we're ready to complete the square.  We take half the linear term, square it, and add it in to both sides.  Our linear term is -6x.  Half of 6 is 3, and 3 squared is 9, so we add 9 to both sides: .  Now we will do the math on the right to get 4, and on the left we will express the perfect square binomial we created while completing this process.  . Now we can move the constant back over by subtraction to get .  Now we can see that the vertex is (3, -4).  Since this is a positive parabola, it opens upwards, like a cup, which means that the lowest part of the parabola, the vertex, is sitting at the bottom, or at a minimum value.  So our answer is C

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