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 = $\frac{-b}{2a}$

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

so x= $\frac{-5}{2(1)}$= -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.