Can this quadratic equation be graphed?

Question

y= -x^2 - 4x- 5

I keep get really weird numbers when I plug in points.

Thanks! I realized I had graphed the vertex as 2, -1.

Answer 1

Yes, it can be graphed. You get really weird numbers when you plug variables in because it never touches the x-axis. Since the x^2 term is negative, you automatically know that the graph is a parabola opening down (like a rainbow). You can also tell the y-intercept easily by setting the x's to zero. This gives the y intercept as y = -5. To get the x intercepts of the parabola, you will set y equal to zero. This gives you a simple quadratic equation which you can use the quadratic formula to solve, since it can't be factored. -x^2-4x-5 solves to
-2+i and -2-i. Since this is a complex number, you automatically know that there are no x intercepts. Now, you have a downward opening parabola with a negative y-intercept that doesn't have x intercepts. Totally graphical, but the numbers will look funny when you try to plug in variables. Just like you describe.

Answer 2

Yes this quadratic eqn can be graphed:

It has a y-int of (0,-5), no x-int, and a vertex of (-2,-1).

Answer 3

All quadratic equations can be graphed. Not all of them will have x-intercepts though, so perhaps you misworded your question.