What is the vertices y=2x^2-12x+23 ?

The vertices y=2x^2-12x+23 is Minimum (3,5)

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vertices y=2x^2-12x+23

vertices

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

Minimum (3, 5)

Solution steps

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

The parabola parameters are:

a = 2, b = - 12, c = 23

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

x_{v} = - \frac{( - 12 )}{2 \cdot 2}

Simplify

x_{v} = 3

Plug in

x_{v} = 3

to find the

y_{v}

value

y_{v} = 5

Therefore the parabola vertex is

(3, 5)

a < 0,

then the vertex is a maximum value

a > 0,

then the vertex is a minimum value

a = 2

Minimum (3, 5)

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

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

y = + (2 x + 1)^{2} - 1

(x + 2)^{2} + 3

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

What is the vertices y=2x^2-12x+23 ?
The vertices y=2x^2-12x+23 is Minimum (3,5)