find the vertex of the parabola y = x^2 - 5x + 8. simplify both coordinates and write them as proper…

Explanation:

Step1: Identify coefficients

For the quadratic function $y = ax^{2}+bx + c$, in $y=x^{2}-5x + 8$, $a = 1$, $b=-5$, $c = 8$.

Step2: Find x - coordinate of vertex

The formula for the x - coordinate of the vertex of a parabola is $x=-\frac{b}{2a}$. Substitute $a = 1$ and $b=-5$ into the formula: $x=-\frac{-5}{2\times1}=\frac{5}{2}$.

Step3: Find y - coordinate of vertex

Substitute $x = \frac{5}{2}$ into the function $y=x^{2}-5x + 8$. So $y=(\frac{5}{2})^{2}-5\times\frac{5}{2}+8=\frac{25}{4}-\frac{25}{2}+8=\frac{25 - 50 + 32}{4}=\frac{7}{4}$.

Answer:

$(\frac{5}{2},\frac{7}{4})$