Question

How do i solve and graph y=x^2+5x+6

Answer 1

slope = 4
y-intercept = 6
hope this helps :)

Answer 2

`y=x^2+5x+6`

To graph this equation we find x intercepts and vertex

To find x intercept we replace y with 0

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

Factor the right hand side

0 = (x+3)(x+2)

x+3 =0 and x+2 =0

x=-3 and x=-3

So x intercept are (-3,0) and (-2,0)

Now we find vertex, vertex formula is x =
`(-b)/(2a)`

`y=x^2+5x+6` , a= 1 and b = 5

so x=
`(-5)/(2(1))`= -2.5

Now plug in -2.5 in
`y=x^2+5x+6`

`y=(-2.5)^2+5(-2.5)+6`= -0.25

So vertex is (-2.5, -0.25)

The value of a=1 that is positive , so parabola opens upwards.

The graph is attached below.