Mathematics: The following equation of a quadratic function is given in standard form. f(x) = x²- 2x + 2 Determine the vertex for each quadratic. Round your answers to the nearest tenth if necessary. (x, y) = .

The following equation of a quadratic function

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01.02.2022

The vertex for each quadratic is (x,y) = (1,1)

Step-by-step explanation:

To determine the vertex for each quadratic,

The vertex of the coordinate can be determined using the formula,

$x-vertex = \frac{-b}{2a}$

The standard form of the quadratic function is

$f(x) = ax^{2} + bx + c$

Hence, for the given equation of the quadratic function,

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

a = 1

b = -2

and c = 2

Hence, x-vertex becomes,

$x-vertex = \frac{-b}{2a}$

$x-vertex = \frac{--2}{2(1)}$

$x-vertex = \frac{2}{2}$

∴ x - vertex = 1

This is the vertex for the x-coordinate

To determine, the vertex for the y-coordinate

We will put the value of the vertex of the x-coordinate in the equation and write

$y-vertex = x^{2} - 2x + 2$

Then,

$y-vertex = (1)^{2} -2(1) + 2$

$y-vertex = 1 - 2 +2\\y-vertex = 1$

This the vertex for the y-coordinate

Hence, (x,y) = (1,1)

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