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

1 Answer
Sep 1, 2017

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]}