Answer:
[tex]y=(x-3)^2-6[/tex]
Step-by-step explanation:
[tex]y=x^2-6x+3[/tex]
This is written in the standard form of a quadratic function:
[tex]y=ax^2+bx+c[/tex]
where:
You need to convert this to vertex form:
[tex]y=a(x-h)^2+k[/tex]
where:
To find the vertex form, you need to find the vertex. For this, use the equation for axis of symmetry, since this line passes through the vertex:
[tex]x=-\frac{b}{2a}[/tex]
Using your original equation, identify the a, b, and c terms:
[tex]a=1\\\\b=-6\\\\c=3[/tex]
Insert the known values into the equation:
[tex]x=-\frac{(-6)}{2(1)}[/tex]
Simplify. Two negatives make a positive:
[tex]x=\frac{6}{2} =3[/tex]
X is equal to 3 (3,y). Insert the value of x into the standard form equation and solve for y:
[tex]y=3^2-6(3)+3[/tex]
Simplify using PEMDAS:
[tex]y=9-18+3\\\\y=-9+3\\\\y=-6[/tex]
The value of y is -6 (3,-6). Insert these values into the vertex form:
[tex](3_{h},-6_{k})\\\\y=a(x-3)^2+(-6)[/tex]
Insert the value of a and simplify:
[tex]y=(x-3)^2-6[/tex]
:Done
