How to find the x and y-intercept given $y = 1/2x^2 - 2$ ?

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Answer 1 · 2015-05-10T13:38:45

This parabola intersects the $y$ axis at $(0, -2)$ and the $x$ axis at $(-2, 0)$ and $(2, 0)$ .

To find these intersections, start by substituting $x = 0$ and $y = 0$ into the equation of the curve.

First the $y$ axis: Substitute $x = 0$ ...

$y = (1/2)x^2 - 2 = (1/2)0^2 - 2 = 0 - 2 = -2$ .

Now the $x$ axis: Substitute $y = 0$ to get:

$(1/2)x^2-2 = 0$

Add 2 to both sides:

$(1/2)x^2 = 2$

Multiply both sides by 2 to get:

$x^2 = 4$

Hence $x = +-2$

How to find the x and y-intercept given y = 1/2x^2 - 2y = 1/2x^2 - 2?