To find the intercepts of y = 2x^2-5x+3 with X and Y axis>

Solution:

The equation of X axis is y = 0 . So intercept of the given curve on x axis is got by putting y= 0 in the equation and solving for x.

0 = 2x^2-5x+3

Factorising the right,

(2x-1)(x-3) = 0. Or

2x-1 = 0 . x-3 = 0.

x =1/2 . Or x= 3 are the two x intercepts.

The y intercept is got by putting x= 0 and solving for y in the given equation of the curve.

y = 2x^2-5x+ 3

y = 2*0^2-5*0+3 = 3.

So y= 3 is the y intercept.

To find the intercepts of a graph with an axis , we have to calculate f(x)=0 and f(0).

When calculating f(x)=0, we'll find the interception of the graph with x axis.

Now, we'll calculate f(x)=0, that means that y=0.

2x^2-5x+3=0

We'll apply the quadratic formula for finding x1 and x2.

x1 = [5+sqrt(25-24)]/4

x1 = (5+1)/4

x1 = 6/4

x1 = 3/2

x2 = (5-1)/4

x2 = 1

The interception points of the graph with x axis are: (1,0) and (3/2,0)

Now, we'll calculate the interception point with y axis and for this reason, we'll put x=0.

y = 2*0-5*0+3

**y = 3**

The interception point of the graph with y axis is: (0,3).

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)