Sketch a graph of the polynomial function f(x) = x2 + 4x2 + 3x. Use it to complete each statement.

The graph of the function crosses the x-axis at x = 0, x = -1, and x = -3  and therefore, f(x) is positive in one of the intervals of the x-intercept

The correct options are;

Reason:

The given function is presented as follows;

f(x) = x³ + 4·x² + 3·x

The graph of the above function is created with MS Excel

From the function, we have; f(x) = x³ + 4·x² + 3·x = x·(x + 3)·(x + 1)

From the graph, we have;

f(x) is negative in the interval -∞ < x < -3, and -1 ≤ x ≤ 0 which gives;

The value of f(x) is increasing on the interval -∞ < x ≤ -2 and also in the interval -0.5 ≤ x ≤ ∞, therefore;

The value of the function f(x) is positive on the interval -3 ≤ x ≤ -1, and also positive in the interval 0 ≤ x < ∞

Therefore;

The value of f(x) is decreasing for values of x between -2 ≤ x ≤ -0.5

Therefore;

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1. f(x) is negative

a 360 degree rotation

step-by-step explanation:

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752