Question

find the vertex by substituting the value of x into the quadratic equation.

Answer 1

Answer:

Vertex = (1, 1)

Explanation:

Given the quadratic equation:

$y-x^2+2x=2$

First, rewrite the equation in the standard form y=ax²+bx+c:

$\begin{gathered} y=x^2-2x+2 \\ \implies a=1,b=-2,c=2 \end{gathered}$

The value of x at the vertex is obtained using the formula for the equation of symmetry below:

$\begin{gathered} x=-\frac{b}{2a} \\ x=-\frac{-2}{2\times1}=1 \end{gathered}$

Next, substitute x=1 into the quadratic function:

$\begin{gathered} y=x^2-2x+2 \\ =1^2-2(1)+2 \\ y=1 \end{gathered}$

The vertex of the quadratic function is (x, y) = (1, 1).

The first option is correct.