Question

unit 5 review
score: 31/71 answered: 8/18
question 9
identify the vertex of the parabola $y = x^2 - 4x + 3$ graphed below
vertex = ( , )

Explanation:

Step1: Recall vertex formula for parabola

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 equation \( y = x^2-4x + 3 \), we have \( a = 1 \), \( b=-4 \), and \( c = 3 \).

Step2: Calculate the x - coordinate of the vertex

Substitute \( a = 1 \) and \( b=-4 \) into the formula \( x =-\frac{b}{2a} \). We get \( x=-\frac{-4}{2\times1}=\frac{4}{2} = 2 \).

Step3: Calculate the y - coordinate of the vertex

Substitute \( x = 2 \) into the equation \( y=x^2-4x + 3 \). Then \( y=(2)^2-4\times(2)+3=4 - 8 + 3=-1 \).

Answer:

\((2, - 1)\)