Find the x-axis intercept and y-axis intercept of the graph y=2x^2-5x+3?

x-axis intercept is the value of y coordinate where the graph intersects the x-axis. At this point value of x coordinate is 0. therefor to get the value of x axis intercept we substitute value 0 for x in the equation of the graph and then solve it for value of y.

Thus, to get value of x intercept substituting value x = 0 in the equation of graph (y = 2x^2 - 5x + 3 = 0)  we get:

y = 2(0^2) - 5*0 + 3 = 0

y = 0 - 0 + 3 = 3

The graph intercepts the x-axis at point (0, 3)

Similarly, to get value of x intercept substituting value y = 0 in the equation of graph we get:

0 = 2x^2 - 5x + 3

This being a quadratic equation there are two roots or values of x. We calculate these as:

x1 = {5 + [(25 - 24)^(1/2)]}/4

= [5 + 1^(1/2)]/4

= (5 + 1)/4 = 6/4 = 1.5

And:

x2 = {5 - [(25 - 24)^(1/2)]}/4

= [5 - 1^(1/2)]/4

= (5 - 1)/4= 4/4 = 1

Thus the graph intercepts the y-axis at two points: (1, 0) and (1.5, 0)