Answered

Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

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

Sagot :

naǫ
[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]

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.