What is the vertices 2x^2-x-1 ?

The vertices 2x^2-x-1 is Minimum (1/4 ,-9/8)

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vertices 2x^2-x-1

vertices

2 x^{2} - x - 1

Minimum (\frac{1}{4}, - \frac{9}{8})

Solution steps

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

The parabola parameters are:

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

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

x_{v} = - \frac{( - 1 )}{2 \cdot 2}

Simplify

x_{v} = \frac{1}{4}

Plug in

x_{v} = \frac{1}{4}

to find the

y_{v}

value

y_{v} = - \frac{9}{8}

Therefore the parabola vertex is

(\frac{1}{4}, - \frac{9}{8})

a < 0,

then the vertex is a maximum value

a > 0,

then the vertex is a minimum value

a = 2

Minimum (\frac{1}{4}, - \frac{9}{8})

2 x^{2} - x - 6

6 x^{2} - 13 x + 6

f (x) = - x^{2} + 3 x - 5

y = x^{2} - 10 x - 4

x^{2} + 6 y = 0