Question

g(x) = x2 + 10x + 25

Sketch the graph of the quadratic function without using a graphing utility. Identify the vertex, axis of symmetry, and x-intercept(s)

Answer 1

I see that the y intercept is 25. Do you see that?

Answer 2

Yes

Answer 3

Also I see that i can be factored:
\[y=(x+5)^2\]
Do you see that?

Answer 4

Yes.

Answer 5

And now that it is in that form I see that it matches perfectly

Answer 6

with the (h,k) form. Do you see that?

Answer 7

Yes I do.

Answer 8

And so the vertex is ???

Answer 9

(-5, 0)

Answer 10

And that makes the axis of symmetry what line?

Answer 11

-5?

Answer 12

Well except that the aos is a line and -5 is not the equation of a line.

Answer 13

So the axis of symmetry is x = -5
And since the factors are (x+5)(x+5) it is clear that x=-5 is a double root which corresponds to a point of tangency to the x axis. And the x intercept (s) are -5

Answer 14

Ok. So the x intercept is just -5 correct?

Answer 15

yep