Question

Brianna is graphing the function f(x) = x2 + 6x + 5. What x-intercepts should Brianna use to graph f(x)?

Answer 1

to find t he x intercepts factor the quadratic and set them = to 0

x^2 +6x+5 = 0

(x+5) (x+1)=0

x+5 = 0   x+1=0

x=-5   x=-1

the x intercepts are -5, x=-1

Answer 2

Hey there!!

We have:

... f(x) = x² + 6x + 5

Remember: f(x) is also called as 'y'.

Hence,

... y = x² + 6x + 5

Now, let's split the middle terms in such a way that, the terms we split 6x into has something common in x² and 5 after grouping.

Let's split 6x with taking the factors of 5.

... 5 = 5 × 1

Hence,

... y = x² + x + 5x + 5

Now taking the common terms,

... y = x(x+1) + 5(x+1)

... y = (x+5)(x+1)

Hence, we got two equations.

... y = x+5 and y = x+1

We have the slope-intercept form:

... y = mx + b

'b' is the y-intercept.

... y-intercept = ( 0,y)

and

... x-intercept = ( x,0 )

... y =x+5

... 0 = x + 5

... -5 = x

and

... y = x+1

... 0 = x+1

... -1 = x

Hence, the x-intercepts are ( 0,-5 ) and ( 0,-1 )

Hope my answer helps!