Question

graph the function on a graphing calculator. use the max or min feature to approximate the vertex.
y₁ = 4x² - 4x + 5
part: 0 / 2
part 1 of 2
the vertex is ( , ).

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 \( Y_1 = 4x^2-4x + 5 \), \( a = 4 \), \( b=-4 \).
So, \( x=-\frac{-4}{2\times4}=\frac{4}{8}=\frac{1}{2}=0.5 \)

Step2: Find the y - coordinate of the vertex

Substitute \( x = 0.5 \) into the function \( Y_1=4x^2-4x + 5 \).
\( Y_1=4\times(0.5)^2-4\times(0.5)+5 \)
\( =4\times0.25-2 + 5 \)
\( =1-2 + 5 \)
\( =4 \)

Answer:

\((0.5,4)\)