Question

Identify the equation of the graph

Answer 1

This has a vertex at (1,-5) and otherwise looks like y=x^2; the two points one x unit away from the vertex are also 1 y unit away, the two points two away are 4 units higher, etc.

$y = (x- 1)^2 - 5$

That's in vertex form. We're not shown any choices; let's multiply this out.

$y = x^2 - 2x - 4$

Either one of those.