You can identify the lines and their colour either by
1. the y-intercepts.
First equation has a y-intercept of 3 and second has a y-intercept of 2.
So first equation is blue, and second is red.
2. the slopes
First equation has a negative slope (so blue), and second has a positive slope (so red).
Now work on each of the equations.
1. first equation (blue)
If we put x=0, we end up with the equation y≤3, the ≤ sign indicates that the region is BELOW the BLUE line.
2. second equation (red).
If we put x=0, we end up with the equation y>2, the > sign indicates that the region is ABOVE the RED line AND the red line should be dotted (full line if ≥).
So at the point, it won't be too hard to find the correct region.
To confirm, take a point definitely in the region, such as (-6,0) and substitute in each equation to make sure that both conditions are satisfied.
Consider f(x) = -4(x - 6)² + 3
This is a parabola with vertex at (6, 3).
Because the leading coefficient of -4 is negative, the curve opens downward, and the vertex is the maximum value.
Answer: Maximum of f(X) = 3
Consider the function g(x) = 2 cos(2x - π) + 4
The maximum value of the cosine function is 1.
Therefore the maximum value of g(x) is
2*1 + 4 = 6
Answer: Maximum of g(x) = 6
Use the Pythagorean theorem to find the third side then add all three sides together
3 : 4 : 5 = 3² : 4² : 5² = 9 : 16 : 25
The answer is B.
Hope this helps.
