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

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