What is the vertices 2x^2+4x-1 ?

The vertices 2x^2+4x-1 is Minimum (-1,-3)

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vertices 2x^2+4x-1

vertices

2 x^{2} + 4 x - 1

Minimum (- 1, - 3)

Solution steps

y = 2 x^{2} + 4 x - 1

The parabola parameters are:

a = 2, b = 4, c = - 1

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

x_{v} = - \frac{4}{2 \cdot 2}

Simplify

x_{v} = - 1

Plug in

x_{v} = - 1

to find the

y_{v}

value

y_{v} = - 3

Therefore the parabola vertex is

(- 1, - 3)

a < 0,

then the vertex is a maximum value

a > 0,

then the vertex is a minimum value

a = 2

Minimum (- 1, - 3)

(x + 2)^{2} = - 12 (y - 5)

2 x^{2} - 8 x + 6

f (x) = x^{2} + 14 x - 72

f (x) = x^{2} + 8 x

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