Question

what are the solution points to graph the following quadratic equation? y=-3x^2-6x-5

Answer 1

The solution points are the points at which the graph intersects the x axis (i.e y=0):
\[-3x^2-6x-5=0\]
Use the quadratic formula to find the values of x.

Answer 2

There are no x intercepts. I need to find other solution points to create the graph. Vertex (-1,-2). I am using excel to create the graph.

Answer 3

Oh yeah the roots are complex, you're right. It's always better when graphing a parabola to write it as:
\[y=-3(x^2+2x+\frac{5}{3}) \implies y=-3(x+1)^2-2 \implies y+2=-3(x+1)^2.\]

Answer 4

The vertex as you said is (-1,-2). Take a point on the right of -1 and another point to the left of it, say 0 and -2. At x=0, y=-5 and at x=-2, y=5 as well. So the two points are (0,-5) and (-2,-5).

Answer 5

Now connect these three points with a parabola opening downward as you know.

Answer 6

x y=-3x^2-6x-5
-10.14 -253.13
-8.037 -150.57
-5.984 -76.52
-3.989 -28.8
-1.936 -4.628
-1 -2
-0.064 -2.377
0 -5
2.053 -29.96
4.048 -78.47
6.042 -150.79
8.213 -256.65
Do the points make sense?

Answer 7

They do, but you don't really need all these points. Two points and the vertex are enough to draw the parabola.

Answer 8

ok thank you

Answer 9

You're welcome.