What is the vertices x^2-6x+10 ?

The vertices x^2-6x+10 is Minimum (3,1)

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vertices x^2-6x+10

vertices

x^{2} - 6 x + 10

Minimum (3, 1)

Solution steps

y = x^{2} - 6 x + 10

The parabola parameters are:

a = 1, b = - 6, c = 10

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

x_{v} = - \frac{( - 6 )}{2 \cdot 1}

Simplify

x_{v} = 3

Plug in

x_{v} = 3

to find the

y_{v}

value

y_{v} = 1

Therefore the parabola vertex is

(3, 1)

a < 0,

then the vertex is a maximum value

a > 0,

then the vertex is a minimum value

a = 1

Minimum (3, 1)

f (x) = x^{2} + 4 x - 3

f (x) = x^{2} + 10 x + 9

y = - 3 x^{2} - 12 x - 9

x^{2} = 8 (y + 4)

y = 3 x^{2} - 12 x + 8