How y intercept is in the negative quadrant?

[user3963]

Hi everyone,

Can someone tell me how the graph is in the negative quadrant. The y-intercept is 2 which should be in the + quadrant and above 0, not below the (0,0)?

[cylverixxx]

Well the sketch is not all that accurate, but for x \in \left[-1, -\frac 23\right] we get that 3x^2 + 5x + 2 \leq 0.

So yeah the region where the quadratic is below the x axis occurs to the left of x = 0 and in that sense you are right.

Here’s the correct graph, if you’re curious: