Question

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) = ______.

Answer 1

Answer:

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 $x$ 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, $(x,y) = (1,1)$