Question

Graph the equation y = x2 + 6x + 5 on the accompanying set of axes. You must
plot 5 points including the roots and the vertex.

Answer 1

Answer:

Please check the graph below.

Step-by-step explanation:

Given the function

$y\:=\:x^2\:+\:6x\:+\:5$

Axis interception points of the function

x-axis interception points can be computed by setting y=0

$x^2+6x+5=0$

$\left(x+1\right)\left(x+5\right)=0$

Using the zero factor principle

if  $\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)$

$x+1=0\quad \mathrm{or}\quad \:x+5=0$

$x=-1,\:x=-5$

Hence,

x-axis interception points are: (-1, 0), (-5, 0)

y-axis interception points can be computed by setting x=0

$x^2+6x+5=0$

$y\:=\:\left(0\right)^2\:+\:6\left(0\right)\:+\:5$

$y=0+0+5$

$y=5$

Hence,

y-axis interception points are: (0, 5)

From the graph, it is clear that at (-3, -4) the parabola changes direction, hence (-3, -4) it the "vertex".

Also at the point x=-2, then y is = -3

So, all the points are labeled and the graph is attached below.