Question

Graph the equation y = x2 + 8x + 15 on the accompanying set of axes. You must
plot 5 points including the roots and the vertex.
Click to plot points. Click points to delete them.

Answer 1

First we find the intersect points with OX (the roots)

$x^{2}$ + 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: