Step-by-step explanation:
2x^2 + x - 28
= 2x^2 - 8x + 7x - 28
= 2x(x-4) +7(x-4)
= (2x+7)(x-4)
2x+7 = 0 or x-4 = 0
x = -7/4 or x = 4
The foci of the hyperbola with equation 5y^2-4x^2=20 will be given as follows:
divide each term by 20
(5y^2)/20-(4x^2)/20=20/20
simplifying gives us:
y^2/4-x^2/5=1
This follows the standard form of the hyperbola
(y-k)²/a²-(x-h)²/b²=1
thus
a=2, b=√5 , k=0, h=0
Next we find c, the distance from the center to a focus.
√(a²+b²)
=√(2²+(√5)²)
=√(4+5)
=√9
=3
the focus of the hyperbola is found using formula:
(h.h+k)
substituting our values we get:
(0,3)
The second focus of the hyperbola can be found by subtracting c from k
(h,k-c)
substituting our values we obtain:
(0,-3)
Thus we have two foci
(0,3) and (0,-3)
we have
using a graph tool
see the attached figure
the domain of the function is all real numbers------> the interval is (-∞,∞)
the range of the function is --------------------------------> the interval (-∞,9]
therefore
the answer is
The range of the function is all real numbers less than or equal to 
A. No because -2*-3=6
B. No because if you plug in 5 it will be 1-2(5) which equals -9
C. No because when you plug in -4 it will be 4+6(-4) which equals to -20
