Question

Which graph is defined by f(x) = x2 + 5|x| + 6?

Answer 1

it is quadratic polynomial graph

Answer 2

y = x² + 5|x| + 6
we know,
|x|² = x² use this ,
y = |x|² + 5|x| + 6
STEP for drawing y = |x|² + 5|x| + 6
step1 :- first draw y = x² + 5x + 6, this graph is quadratic equation .

step2 :- Leave the part of y=x² + 5x + 6 right side to y- axis and also take its image with respect to y - axis as plane mirror .

step3 :- now remove the part of y = x² + 5x + 6 to left side from y - axis .

now your graph is ready
you can see in figure .