What is the vertex form of #y= (x-3)(x-4) #?

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Answer 1 · 2016-01-09T03:47:46

Multiply out and then complete the square to find the vertex form.

y = (x - 3)(x - 4)

y = #x^2# - 3x - 4x + 12

y = #x^2# - 7x + 12

y = 1(#x^2# - 7x + m - m) + 12

m = #(b / 2)^2#

m = #(-7/2)^2#

m = #49/4#

y = 1(#x^2# - 7x + #49/4# - #49/4#) + 12

y = 1#(x^2 - 7/2)^2# - #1/4#

The vertex form of y = (x - 3)(x - 4) is y = 1#(x^2 - 7/2)^2# - #1/4#

Below I have included 2 problems that you may do to practice yourself with the completion of square technique.

a) y = (2x + 5)(x - 6)

b) y = #3x^2# + 7x - 9