Question

Which equation is y=-6x2 + 3x + 2 rewritten in vertex form?

O y=-6(x-1)2+8
O y =
+
13
8
y=-8(x+4)
y=-6-
2
O y=-6 -
19
8
Y=
X-
7
2

Answer 1

The vertex form of the equation is:

`y=-6\,(x-(1)/(4))^2+(19)/(8)`

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:

`y=ax^2+bx+c`

is given by:

`x_(vertex)=(-b)/(2\,a)`

which in our case renders:

`x_(vertex)=(-b)/(2\,a)\\x_(vertex)=(-3)/(-12)\\x_vertex=(1)/(4)`

Knowing this, then the y-coordinate of the vertex is obtained by using the x-coordinate of the vertex in the functional form:

`y=-6\,((1)/(4)) ^2+3\,((1)/(4) )+2=(19)/(8)`

Then, the equation of the parabola in vertex form becomes:

`y=a\,(x-(1)/(4))^2+(19)/(8)`

Now we need to find the value of the parameter
, 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:

`y=-6\,(x-(1)/(4))^2+(19)/(8)`