Question

How do you graph `2x ^ { 2} + 4y + 3= 5`?

Answer 1

This is an inverted parabola, with vertex `(0, 1/2)` and `x` intercepts `(-1, 0)` and `(1, 0)`.

Explanation:

Given:

`2x^2+4y+3=5`

Subtract `2x^2+3` from both sides to get:

`4y = -2x^2+2`

Divide both sides by `4` to get:

`y = -1/2 x^2+1/2 = -1/2(x^2-1) = -1/2(x-1)(x+1)`

Note that the coefficient of `x^2` is negative, so this is roughly an upside-down U shape parabola, with vertex at `(0, 1/2)` (which is also the `y` intercept, axis `x=0` and `x` intercepts `(-1, 0)` and `(1, 0)`.

So it looks like this:
graph{y = -1/2x^2+1/2 [-5.084, 4.916, -2.48, 2.52]}