Question

question 9 of 10
find the vertex of the function given below.
y = x² - 6x + 1

a. (3, -8)
b. (4, 1)
c. (1, 5)
d. (2, -3)

Explanation:

Step1: Recall the vertex formula for a quadratic function

For a quadratic function in the form \( y = ax^2+bx + c \), the x - coordinate of the vertex is given by \( x=-\frac{b}{2a} \). In the function \( y=x^{2}-6x + 1 \), we have \( a = 1 \), \( b=-6 \) and \( c = 1 \).

Step2: Calculate the x - coordinate of the vertex

Using the formula \( x=-\frac{b}{2a} \), substitute \( a = 1 \) and \( b=-6 \) into it. We get \( x=-\frac{-6}{2\times1}=\frac{6}{2}=3 \).

Step3: Calculate the y - coordinate of the vertex

Substitute \( x = 3 \) into the function \( y=x^{2}-6x + 1 \). Then \( y=(3)^{2}-6\times3 + 1=9-18 + 1=-8 \).

Answer:

A. (3, -8)