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Answer:
D.
Step-by-step explanation:
The point-slope form of a line is given by:
The line given to us has equation; .
The slope of this line is -4. The of the line perpendicular to this line is the negative reciprocal of the slope of the given line.
Our slope of interest is therefore;
Since the point goes through (-2,7), we have .
We plug in the slope and the point into the point-slope formula to obain;
The required equation is:
Answer:
The function f(x) is positive in the interval (-≠,-2.5) ∪ (1,∞)
Step-by-step explanation:
we have
This is a vertical parabola open upward (the leading coefficient is positive)
The vertex is a minimum
The coordinates of the vertex is the point (h,k)
step 1
Find the vertex of the quadratic function
Factor the leading coefficient 2
Complete the square
Rewrite as perfect squares
The vertex is the point (-\frac{3}{4},-\frac{49}{8})
step 2
Find the x-intercepts (values of x when the value of f(x) is equal to zero)
For f(x)=0
take the square root both sides
therefore
The function f(x) is negative in the interval (-2.5,1)
The function f(x) is positive in the interval (-≠,-2.5) ∪ (1,∞)
see the attached figure to better understand the problem
