Review question

# What does the curve $x^4-y^2=y+1$ look like? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8855

## Solution

Which of the following sketches is a graph of $x^4-y^2=2y+1$?

The equation rearranges to $x^4 = y^2 + 2y + 1 = (y+1)^2$ which is true if and only if $x^2=y+1 \qquad \text{or} \qquad -x^2=y+1.$

So the graph consists of two parabolae, $y=x^2-1$ and $y=-x^2-1$, which both cross the $y$-axis at $y=-1$, and so form the graph in (b).