Answer:
a. x= -4 x=2
b. (-1,-9)
c. [-9,∞)
d. x=-1
Step-by-step explanation:
To find the roots or x intercepts, you set the parabola equal to 0 and solve.
0=+2x-8 which will equal (x+4)(x-2) so x= -4, 2
To find the vertex you will do , a=1 and b=2 so
which equals x= -1, to find the y value, you will plug x into the equation
y=+2(-1)-8 which means y=-9 so the vertex is (-1,-9)
The range is bottom to top so it is [-9,∞)
the AOS is equal to the x value of the vertex so x= -1
The equation of f(x) is f(x) = x + 4
<h3>How to determine the equation?</h3>The given parameters are
f(-1) = 3 and f(1) = 5
Start by calculating the slope (m) using:
This gives
Evaluate
m = 1
The equation is then calculated as;
f(x) = m(x - x1) + f(-1)
This gives
f(x) = 1(x + 1) + 3
Expand
f(x) = x + 4
Hence, the equation of f(x) is f(x) = x + 4
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Both functions decrease at (-1, 2)
<h3>How to determine the decreasing intervals of the function?</h3>The complete question is added as an attachment
The polynomial function f(x) is represented by the graph.
From the graph, the polynomial function decreases at (-2, 2)
The absolute function is given as;
f(x) = =5|x + 1| + 10
The vertex of the above function is
Vertex = (-1, 10)
Because a is negative (a= -5), the vertex is a maximum.
This means that the function decreases at (-1, ∞)
So, we have
(-2, 2) and (-1, ∞)
Combine both intervals
(-1, 2)
This means that both functions decrease at (-1, 2)
See attachment 2 for the number line that represents the interval where both functions are decreasing
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