Quadratic Function
The general form of a quadratic equation is:
[tex]y=ax^2+bx+c[/tex]Comparing this equation with the given function:
[tex]y=1x^2+bx+c[/tex]It's clear that
a=1
We don't know the values of b and c.
To find them, we use the vertex form of the quadratic equation:
[tex]y=a\mleft(x-h\mright)^2+k[/tex]Where the point (h,k) are the coordinates of the vertex.
Substituting the coordinates of the vertex (3,8):
[tex]y=a(x-3)^2+8[/tex]Expanding the square and substituting a=1:
[tex]y=x^2-6x+9+8=x^2-6x+17[/tex]The equation is now in standard form, and we can easily identify the values of b and c:
b = -6
c = 17
