What is the vertices f(x)=3x^2-2x-1 ?

The vertices f(x)=3x^2-2x-1 is Minimum (1/3 ,-4/3)

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vertices f(x)=3x^2-2x-1

vertices

f (x) = 3 x^{2} - 2 x - 1

Minimum (\frac{1}{3}, - \frac{4}{3})

Solution steps

y = 3 x^{2} - 2 x - 1

The parabola parameters are:

a = 3, b = - 2, c = - 1

x_{v} = - \frac{b}{2 a}

x_{v} = - \frac{( - 2 )}{2 \cdot 3}

Simplify

- \frac{- 2}{2 \cdot 3} : \frac{1}{3}

x_{v} = \frac{1}{3}

Plug in

x_{v} = \frac{1}{3}

to find the

y_{v}

value

y_{v} = - \frac{4}{3}

Therefore the parabola vertex is

(\frac{1}{3}, - \frac{4}{3})

a < 0,

then the vertex is a maximum value

a > 0,

then the vertex is a minimum value

a = 3

Minimum (\frac{1}{3}, - \frac{4}{3})

7 x^{2} - 40 x - 25

f (x) = (x - 3)^{2} - 1

f (x) = x^{2} + 6 x + 7

y = 2 x^{2} - 12 x + 23

f (x) = (x - 3)^{2} + 2

What is the vertices f(x)=3x^2-2x-1 ?
The vertices f(x)=3x^2-2x-1 is Minimum (1/3 ,-4/3)