How do you find the axis of symmetry, vertex and x intercepts for y=x^2+6x+5?

1 Answer
Apr 12, 2017

Axis of symmetry: x=-3
Vertex: (-3,-4)
X-intercepts: x=-5 and x=-1

Explanation:

Axis of symmetry:-
Can be found by applying x=-b/(2a)
In the equation y=color(red)1x^2+color(blue)6x+color(green)5, a=1, b=6, c=5
So, x=-6/(2(1))=color(purple)(-3)

Vertex:-
we substitute the x value (color(purple)(-3)) we found in the axis of symmetry in the function, and we will get
(-3)^2+6(-3)+5=9-18+5=color(magenta)(-4),
The vertex is the point (color(purple)(-3), color(magenta)(-4))

X-intercepts:-
X-intercept is when y=0, which means x^2+6x+5 should be equal to zero.
x^2+color(orange)6x+color(grey)5=0
Now we can factor it by this way since the coefficient of x^2 is 1, what two numbers if multiplied will give you color(grey)5 and if added will give you color(orange)6? They are color(brown)5 and color(darkblue)1, so,
(x+color(brown)5)(x+color(darkblue)1)=0
x+5=0 and x+1=0
x=-5 and x=-1