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2 answers:
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Answer:
a. The function is increasing for all real values of x where x < –4.
Step-by-step explanation:
Let me help you, I have answered this question once in Brainly as well
Given the factored form of the function:
f(x) = -(x + 6)(x+2)
<=> f(x) =
We will convert to vertex form
Let analyse other possible answers:
<u>a. The function is increasing for all real values of x where x < –4.</u>
True, because the parameter a = - 1 so the graph open down all over its domain
<u>b. The function is increasing for all real values of x where –6 < x < –2.</u>
Wrong, the function decrease in the interval from –4.< x < -2
<u>c. The function is decreasing for all real values of x where x < –6 and where x > –2.</u>
Wrong, the function increase in the interval from -6 < x < -4
<u>d. The function is decreasing for all real values of x where x < –4.</u>
Wrong, The function is increasing for all real values of x where x < –4.
The distance from point A(−9,−3) to the line y = x−6 is 8.5 units
<u>What is slope ?</u>
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
step 1
Find the slope of the perpendicular line to the given line
y=x-6 ---> given line
The slope is m=1
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
m1*m2 = -1
we have
m1=1
substitute
(1)*m2 = -1
so
m2 = -1
step 2
Find the equation of the perpendicular line to the given line
The equation in point slope form is
y-y1=m(x-x1)
we have
m=-1
(x1,y1)=(−9,−3)
substitute
y+3=-1(x+9)--> equation in point slope form
y+3= -x-9
y= -x-12---> equation in slope intercept form
step 3
Find the intersection point between the given line and the perpendicular line to the given line
we have the system of equations
y = x−6.
y= -x-12
Solve the system by graphing
The intersection point is (-3,-9)
see the attached figure
step 4
we know that
The distance between the point A and the point (-3,-9) is the same that the distance between point A and the line y=x-6
the formula to calculate the distance between two points is equal to
d=√[(y2-y1)² + (x2-x1)²]
substitute the values
d=√[(-9+3)² + (-3+9)²]
d= √72 units
simplify
d= 6√2 = 8.5 units
To learn more about the slope from the given link
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