We can find the #x#-coordinate of the vertex by using the formula #-\frac{b}{2a}#, where #a# and #b# come from the standard form of #ax^2+bx+c#.

In this equation,

Plugging in yield:

#-\frac{-3}{2(1)}\quad\implies\quad \frac{3}{2}#

To find the #y#-coordinate of the vertex, plug the #x#-coordinate into the equation in standard form:

#x^2-3x+8#

#\implies (\frac{3}{2})^2-3(\frac{3}{2})+8#

#\implies \frac{9}{4}-\frac{9}{2}+8#

#\implies -\frac{9}{4}+8#

#\implies \frac{23}{4}#

#\therefore# the vertex is #(\frac{3}{2},\frac{23}{4})#.

The #y#-intercept is simply #(0,c)#, which is #(0,8)# in this case.

For a third point, we can find the axis of symmetry of the parabola, and reflect the #y#-intercept across that line.

The axis of symmetry is the vertex’s #x#-coordinate, which is #1.5#.

#\therefore# the third point will have an #x#-coordinate of #1.5\cdot 2#, which is #3#. The #y#-coordinate is the same as the #y-#-intercept, which is #8#.

#\therefore# a third point is #(3,8)#.

That’s all we need to graph a parabola.