Question 2.6.6: Find the vertex of the parabola y=2x²-6x+4....

We considered this parabola in Example 3 and found the vertex by completing the square. We shall use the vertex formula with a=2 and b=-6, obtaining the x-coordinate
\frac{-b}{2 a}=\frac{-(-6)}{2(2)}=\frac{6}{4}=\frac{3}{2}.

We next find the y-coordinate by substituting \frac{3}{2} for x in the given equation:
y=2\left(\frac{3}{2}\right)^2-6\left(\frac{3}{2}\right)+4=-\frac{1}{2}

Thus, the vertex is \left(\frac{3}{2},-\frac{1}{2}\right) (see Figure 5).