What is the vertices y=2x^2-4x+7 ?

The vertices y=2x^2-4x+7 is Minimum (1,5)

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vertices y=2x^2-4x+7

vertices

y = 2 x^{2} - 4 x + 7

Minimum (1, 5)

Solution steps

y = 2 x^{2} - 4 x + 7

The parabola parameters are:

a = 2, b = - 4, c = 7

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} = 5

Therefore the parabola vertex is

(1, 5)

a < 0,

then the vertex is a maximum value

a > 0,

then the vertex is a minimum value

a = 2

Minimum (1, 5)

y = (x + 3) (x - 3)

f (x) = - 3 x^{2} - 18 x - 25

y = 18 x^{2} - 14 x + 9

f (x) = - 3 x^{2} + 18 x - 8

y = x^{2} - 6 x + 8