What is the vertices f(x)=x^2-6x+9 ?

The vertices f(x)=x^2-6x+9 is Minimum (3,0)

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vertices f(x)=x^2-6x+9

vertices

f (x) = x^{2} - 6 x + 9

Minimum (3, 0)

Solution steps

y = x^{2} - 6 x + 9

The parabola parameters are:

a = 1, b = - 6, c = 9

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} = 0

Therefore the parabola vertex is

(3, 0)

a < 0,

then the vertex is a maximum value

a > 0,

then the vertex is a minimum value

a = 1

Minimum (3, 0)

x^{2} + x + 1

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

f (x) = 3 (x + 2)^{2} + 1

- 2 x^{2} + 8 x - 1

y = x^{2} + 3 x

What is the vertices f(x)=x^2-6x+9 ?
The vertices f(x)=x^2-6x+9 is Minimum (3,0)