CHILDREN OF OPENSTUDY

Sketch the graph of y=x^2+6x+5 giving the equation of the axis of symmetry and the co-ordinates of the vertex.

Question

CHILDREN OF OPENSTUDY

Sketch the graph of y=x^2+6x+5 giving the equation of the axis of symmetry and the co-ordinates of the vertex.

anonymous · Answer

Are you able to do some of the question or do you need help with all of it?

anonymous · Answer

Well there is something that you need to do to it, and then I can do it. But in class everyone was going 'you need to square it out' or something, but I just left them ones out.

anonymous · Answer

To sketch it just examine the equation. The constant term (+5) tells you the y-intercept. The fact that you have a positive $x^2$ mean that the graph will be a 'U' shape. If you factorise the equation you get $y=(x+5)(x+1)$, and if you set $y=0$ (to see where the graph crosses the $x$ axis) you can see that this will be when $x=-5$ and $x=-1$. That is enough information to sketch the graph.

To find the equation of the axis of symmetry and the co-ordinates of the vertex, you need to find the minimum point of the graph, i.e. where the derivative equals 0. If you differentiate you get:
$\frac{\delta y}{\delta x} = 2x+6$
If you set this equal to zero you have: $2x=-6$ so $x=-3$. You can now substitute this into the equation of the graph to find the corresponding $y$ co-ordinate of the minimum:
$y=(-3)^2 +6(-3)+5=9-18+5=-4$
So the vertex is at $(-3, -4)$.

I'm not sure what they mean by the axis of symmetry, but this graph is quadratic so the line of symmetry will just be the vertical line passing through that minimum point.

Do you understand all of that? Feel free to ask any more questions if you're still stuck.