math
posted by John on .
f(x) = x^2 + 10x + 24
=(x^2 + 10x)+ 24
=(x^2 + 10x + 25  25) + 24
f(x) =(x+5)^2  1
Vertex: (5, 1)
How do you sketch this? I know that in the graph one of the coord is (5, 1) but how do I find the others in order to make a parabola? :

Factorize to get the zeroes:
f(x)=x²+10x+24=(x+6)(x+4)
Therefore the zeroes at at x=6, x=4.
The yintercept is y=24 (= constant term)
The coefficient of x² is positive, so the curve is concave upwards.
The vertex is the minimum of the parabola, and x=5 passing through the vertex is the axis of symmetry.
That should give enough information to sketch the graph?