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Write the quadratic equation y=(x^2)-6x+7 in vertex form

Sagot :

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[tex]x^2-6x+7= \\ x^2-6x+9-9+7= \\ (x-3)^2-9+7= \\ (x-3)^2-2 \\ \\ \boxed{y=(x-3)^2-2}[/tex]

Answer:

[tex]\text{The vertex form is }y=(x-3)^2-2[/tex]

Step-by-step explanation:

Given a quadratic equation  [tex]y=x^2-6x+7[/tex]

we have to write the equation in vertex form.

Comparing given equation with the standard equation [tex]y=ax^2+bx+c[/tex], we get

a=1, b=-6 and c=7

[tex]h=x_{vertex}=\frac{-b}{2a}=\frac{6}{2}=3[/tex]

Substitute the value of x in given equation,

[tex]k=y_{vertex}=1(3)^2-6(3)+7=9-18+7=-2[/tex]

Now, put above values in vertex form of quadratic equation i.e

[tex]y=a(x-h)^2+k[/tex]

[tex]y=1(x-3)^2-2[/tex]

Hence, the vertex form is

[tex]y=(x-3)^2-2[/tex]

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