Question

The graph of the function f(x) = (x + 2)(x + 6) is shown below. On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 4, negative 4), and goes through (negative 2, 0). Which statement about the function is true? The function is positive for all real values of x where x > –4. The function is negative for all real values of x where –6 < x < –2. The function is positive for all real values of x where x < –6 or x > –3. The function is negative for all real values of x where x < –2.

Answer 1

Answer:

Here's your answer

Step-by-step explanation:

we have

f(x)=(x+2)(x+6)f(x)=(x+2)(x+6)

This function represent a quadratic equation (vertical parabola open upward)

The vertex represent a minimum

using a graphing tool

see the attached figure

The x-intercepts are x=-6 and x=-2

The y-intercept is the point (0,12)

The vertex is the point (-4,-4)

The domain is the interval -----> (-∞,∞) (All real numbers)

The range is the interval -----> [-4,∞) (All real numbers greater than or equal to -4)

The function is positive for x < -6 or x > -2

The function is negative for the interval (-6,-2) ----> –6 < x < –2

therefore

The function is negative for all real values of x where –6 < x < –2

Answer 2

Answer:

All are true

Step-by-step explanation:

We have

$f(x)=(x+2)(x+6)$

This is the equation of the parabola with an upward direction having

$x$-intercepts - $x=-6$ and $x=-2$

$y$ -intercept - $(0,12)$

Vertex -  $(-4,-4)$

• The function is positive for all real values of x where x > –4 as the range of the function is [-4,∞)

• The function is negative for the interval $(-6,-2)$

• The function is positive for $x < -6$ or $x > -3$
• Since the function is negative for the interval $(-6,-2)$ , hence function is negative for all real values of $x$  where $x < -2$ .

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