Question

How do you use the important points to sketch the graph of `f(x)= x^2+10x-8`?

Answer 1

I would complete the square.

Explanation:

Completing the square will tell us the roots first of all, a nice basis to sketch the graph.

`therefore` `f(x) = (x+5)^2 -25-8`
`=(x+5)^2-33`

Now we solve the completed square...
`(x+5)^2-33=0`
`(x+5)^2=33`
`(x+5)= +-sqrt33`
`x=-5+-sqrt33`
Now we have our two roots.

The completed square also gives a minimum (as the quadratic is a positive function).

`(x+5)^2-33` has a minimum turning point at `(-5,-33)`

Lastly, the constant of the equation will give us the y intercept, in this case a y intercept at `(0,-8)`

Now we sketch a graph, by plotting these points and drawing a nice smooth curve. graph{y=x^2 +10x-8 [-14.68, 5.32, -37.21, -27.21]}