Sketch the graph parabolas.

g ( x ) = 3x² - 6 x + 5

Solution

For this parabola we've obtain a = 3 , b = -6 and c = 5 .  Ensure that you're cautious with signs while identifying these values.  Thus we know that this parabola will open up as a is positive.

Following are the evaluations for the vertex.

x = -6/2(3)= -6/6=1

y = g (1) = 3 (1)² - 6 (1) + 5 = 3 - 6 + 5 = 2

Then the vertex is (1, 2).  Now at this point we also know that there won't be any x-intercepts for this parabola as the vertex is above the x-axis & it opens upward.

The y-intercept is (0, 5) and by using the axis of symmetry we know that ( 2, 5) have to also be on the parabola.

Following is a sketch of the parabola.