Answer:
Standard form of [tex]f(x) =(x-3)^2 + 6[/tex] is [tex]\mathbf{x^2-6x+15}[/tex]
Step-by-step explanation:
Convert from vertex form to standard form [tex]f(x) =(x-3)^2 + 6[/tex]
If the vertex form is: [tex]a(x-h)^2+k[/tex]
The Standard form is: [tex]ax^2+bx+c[/tex]
Now, converting [tex]f(x) =(x-3)^2 + 6[/tex] into standard form
We know that: [tex](a-b)^2=a^2-2ab+b^2[/tex]
Using the formula:
[tex]f(x) =(x-3)^2 + 6\\f(x)=x^2-2(x)(3)+9+6\\f(x)=x^2-6x+15[/tex]
So, Standard form of [tex]f(x) =(x-3)^2 + 6[/tex] is [tex]\mathbf{x^2-6x+15}[/tex]
