Answer:
The vertex form of the equation is:
[tex]y=-6\,(x-\frac{1}{4})^2+\frac{19}{8}[/tex]
Step-by-step explanation:
In order to write the equation in vertex form, we need to find the vertex coordinates. The x-coordinate of the vertex of a parabola of the form:
[tex]y=ax^2+bx+c[/tex]
is given by:
[tex]x_{vertex}=\frac{-b}{2\,a}[/tex]
which in our case renders:
[tex]x_{vertex}=\frac{-b}{2\,a}\\x_{vertex}=\frac{-3}{-12}\\x_vertex=\frac{1}{4}[/tex]
Knowing this, then the y-coordinate of the vertex is obtained by using the x-coordinate of the vertex in the functional form:
[tex]y=-6\,(\frac{1}{4}) ^2+3\,(\frac{1}{4} )+2=\frac{19}{8}[/tex]
Then, the equation of the parabola in vertex form becomes:
[tex]y=a\,(x-\frac{1}{4})^2+\frac{19}{8}[/tex]
Now we need to find the value of the parameter [tex]"a"[/tex], which since it is the actual leading term of the function in standard form, should be "-6".
Then the vertex form of the equation is:
[tex]y=-6\,(x-\frac{1}{4})^2+\frac{19}{8}[/tex]
