What is the vertices y-2=(x-1)^2 ?

The vertices y-2=(x-1)^2 is Minimum (1,2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

vertices y-2=(x-1)^2

vertices

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

Minimum (1, 2)

Solution steps

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

Rewrite

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

in the form

y = a x^{2} + b x + c

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

The parabola parameters are:

a = 1, b = - 2, c = 3

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

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

Simplify

x_{v} = 1

Plug in

x_{v} = 1

to find the

y_{v}

value

y_{v} = 2

Therefore the parabola vertex is

(1, 2)

a < 0,

then the vertex is a maximum value

a > 0,

then the vertex is a minimum value

a = 1

Minimum (1, 2)

y = (x - 5)^{2}

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

x^{2} - 16

2 x^{2} + 2 x - 4

x^{2} + 2 x + 3