Question

question 2 of 10
find the vertex of the function given below.
y = x² - 2x + 1
a. (1, 0)
b. (2, -3)
c. (-2, 13)
d. (1, 1)

Explanation:

Step1: Recall vertex formula for parabola

For a quadratic function \( y = ax^2+bx + c \), the x - coordinate of the vertex is given by \( x=-\frac{b}{2a} \). In the function \( y=x^{2}-2x + 1 \), \( a = 1 \), \( b=-2 \), \( c = 1 \).

Step2: Calculate x - coordinate of vertex

Substitute \( a = 1 \) and \( b=-2 \) into the formula \( x=-\frac{b}{2a} \). We get \( x=-\frac{-2}{2\times1}=\frac{2}{2} = 1 \).

Step3: Calculate y - coordinate of vertex

Substitute \( x = 1 \) into the function \( y=x^{2}-2x + 1 \). Then \( y=(1)^{2}-2\times(1)+1=1 - 2 + 1=0 \).

Answer:

A. (1, 0)