Graph the equation.
y
=
2
(
x
−
4
)
2
+
5
y=2(x−4)
2
+5

Step-by-step explanation:

I believe you meant y = 2(x − 4)^2 + 5.  Use the symbol ' ^ " to indicate exponentiation.  This equation has the vertex form of the equation of a quadratic.  The  x-coordinate of the vertex is 4 and the y-coordinate is 5.  Thus, the vertex is at (4, 5).  The multiplier 2 stretches the graph vertically by a factor of 2.

To aid us in graphing this function, find the x- and y-intercepts:

If x = 0, y = 2(-4)^2 + 5, or 37.  Therefore the y-intercept is at (0, 37).  

If y = 0, then

2(x − 4)^2 + 5 = 0,

2(x − 4)^2 = -5  But a square cannot be negative, so there is no x-intercept in this case.

To graph this function, plot the vertex (4, 5) and the y-intercept (0, 37).  Take advantage of symmetry and find another point across x = 4 from (0, 37):  It is (8, 37).

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.