What are the y and x intercept(s) of y=2x^2-4?

3 Answers
Sep 29, 2016

We can set alternately x=0 and y=0 to find the intercepts:

Explanation:

To find the y-intercept set x=0 into your expression and get:
y=2*0-4=-4
Sothe coordinates of the y-intercept will be:
x=0 and y=-4

To find the x-intercept(s) set y=0 to get:
2x^2-4=0
Rearranging:
x^2=4/2
x^2=2
x=+-sqrt(2)
We have two intercepts of coordinates:
x=sqrt(2) and y=0
x=-sqrt(2) and y=0

Graphically we can "see" them:
graph{2x^2-4 [-8.625, 11.375, -6.64, 3.36]}

Sep 29, 2016

y-intercept: y=-4
x-intercepts: x=-sqrt(2) and x=sqrt(2)

Explanation:

The y-intercept is the value of y when x=0
color(white)("XXX")y=2x^2-4 with x=0 becomes
color(white)("XXX")y=2 * 0^2-4 = -4

The x-intercepts are the values of x when y=0
color(white)("XXX")y=2x^2-4 when y=0 becomes
color(white)("XXX")0=2x^2-4
color(white)("XXX")2x^2=4
color(white)("XXX")x^2=2
color(white)("XXX")x=+_sqrt(2)

Sep 29, 2016

y intercept -4, x intercepts +-sqrt2

Explanation:

y=2x^2-4

The y intercept is at x=0
Where: y=-4

The x intercept ia at y=0
Where: 2x^2-4=0

x^2=4/2

x=+-sqrt2

These can be seen on the graph of 2x^2-4 below
graph{2x^2-4 [-6.1, 6.384, -5.12, 1.126]}