What is the vertices y=2x^2-4x+5 ?

The vertices y=2x^2-4x+5 is Minimum (1,3)

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vertices y=2x^2-4x+5

vertices

y = 2 x^{2} - 4 x + 5

Minimum (1, 3)

Solution steps

y = 2 x^{2} - 4 x + 5

The parabola parameters are:

a = 2, b = - 4, c = 5

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)

y = 6 x^{2} - 1

(x + 5)^{2} = - 20 (y - 2)

7 x^{2} - 10 x + 5

f (x) = - 2 x^{2} + 80 x - 10

y = 6 x^{2} - 7 x - 3