The graph of the function f (x) = x2 + 8x + 12 is shown. Which statements describe the graph? Check all that apply.

The vertex is the maximum value.

The axis of symmetry is x = - 4.

The domain is all real numbers.

The range is all real numbers.

The function is increasing over (-∞, - 4).

The x-intercepts are at (-6, 0) and (-2, 0).

De graph ain't shown but we can use some math to solve anyway

the x value of the vertex is also the axis of symmetry

domain is x values

range is y values

if quadratic coefient is positive then it opens up and vertex is min

if it is negative then it is max

x intercept is where y=0

increasing is to the right of vertex for open up and increasing it to the left of vertex for open down

so

x value of vertex from

y=ax^2+bx+c is - b/2a

given1x^2+8x+12

x value is - 8 / (2*1) = - 8/2=-4

axis of symmetry is - 4

to find y value, evaluate f (-4)

f (-4) = (-4) ^2+8 (-4) + 12

f (-4) = 16-32+12

f (-4) = - 4

vertex is (-4,4)

domain is all real

f (x) = 1x^2+8x+12

quadrait coefitent is positive so it opens up and vertex is min

so it is increasing from - 4 to poisitive inifnty

and tosolve

0=x^2+8x+12

0 = (x+6) (x+2)

0=x+6

-6=x

0=x+2

-2=x

x ints are at (-6,0) and (-2,0)

domain is all real (did I say that already)

since there is a minimum at y=-4, the range doesn't extend to all real (example, like y=-5)

so answers are

axis of symmetry is x=-4

domain is all real numbers

x intercepts are at (-6,0) and (-2,0)