Question

Y = 3 x ^ 2 -4x + 1find the vertex of the function. convert to vertex form

Answer 1

`y=3x^2-4x+1`

To find the vertex of a parabola (quadratic equiation) you use the next:

1. Find the axis of simetry (value of x in the vertex) with the next formula:

`\begin{gathered} y=ax^2+bx+c \\ \\ x=(-b)/(2a) \end{gathered}`

For the given equation:

b=-4

a=3

`x=(-(-4))/(2(3))=(4)/(6)=(2)/(3)`

Axis of simetry x=2/3

2. Find the value of y in the vertex. Use the axis of simetry:

`\begin{gathered} y=3((2)/(3))^2-4((2)/(3))+1 \\ \\ y=3((4)/(9))-(8)/(3)+1 \\ \\ y=(12)/(9)-(8)/(3)+1 \\ \\ y=(4)/(3)-(8)/(3)+(3)/(3) \\ \\ y=-(1)/(3) \end{gathered}`3. The vertex is (2/3 , -1/3)

4. Write in vertex form.

General vertex form of a quadratic equation:

`y=a(x-h)^2+k`

The vertex is (h,k)

For the given equation:

a=3

h=2/3

k= -1/3

Equation in vertex form:
`y=3(x-(2)/(3))^2-(1)/(3)`