First we find the intersect points with OX (the roots)
[tex]x^{2}[/tex] + 8x + 15 = 0
delta = 64 - 60 = 4
x12 = (-8 +- 2) /2
x1 = -5 => A(-5,0) is root
x2 = -3 => B(-3,0) is another root
We can find the intersect with OY too by making x=0
so calculate f(0) = 0 + 0 + 15 => C(0,15) is the intersect with OY
The vertex's coords have the following formula: D(-b/2a ; -delta / 4a)
so have the coords D(-8/2 , -4/4) = D(-4 , -1)
We need one more point so we choose a random x
Let x be -2
f(1) = 4 -16 + 15 = 3 => E(-2,3) is a point of the graph
There is the function to help you visualise it:
