How do you graph and identify the vertex and axis of symmetry for 5/2x(x-3)?

1 Answer
Jan 14, 2018

If y=5/2x(x-3) then you can put it into the form of y=ax^2+bx+c to create a table of points, then plot them on the graph.

But since you've already factorised it, you can find the solutions (x-intercepts)
0=5/2x(x-3)
0=5/2x or 0=x-3
x=0 or x=3

The x-intercepts of your graph along with your vertex can allow you to plot a substantially accurate graph.

To find the vertex, complete the square:
y=5/2x(x-3)
y=5/2x^2-15/2x
y=5/2(x^2-3x)
y=5/2(x^2-3x+(3/2)^2-(3/2)^2)
y=5/2((x-3/2)^2-9/4)
y=5/2(x-3/2)^2-45/8

Your vertex then becomes (3/2, -45/8)
which is the same as (1.5, -5.625)
And your axis of symmetry x=1.5