We can write the function in terms of y rather than h(x)
so that:
y = 3 (5)^x
A. The rate of change is simply calculated as:
r = (y2 – y1) / (x2 – x1) where r stands for rate
Section A:
rA = [3 (5)^1 – 3 (5)^0] / (1 – 0)
rA = 12
Section B:
rB = [3 (5)^3 – 3 (5)^2] / (3 – 2)
rB = 300
B. We take the ratio of rB / rA:
rB/rA = 300 / 12
rB/rA = 25
So we see that the rate of change of section B is 25
times greater than A
With the facts you got here, you can make the following equation:
x*(x+2)=24
x^2+2x=24
x^2+2x-24=0
Then you can use the following formula (which you might have seen before):
x = (-b +/- sqrt(b^2-4ac))/2a
where
ax^2+bx+c=0
(-2 +/- sqrt(4+96))/2
(-2 +/- 10)/2
x_1 = 4
x_2 = -6
f(x) + c -> up by c
f(x) - c -> down by c
f(x + c) -> left by c
f(x - c) -> right by c
For y = f(x + c), the y value of x now takes the y value of the function of x + c, or the one c to the right of x, shifting the entire graph left by c.
<h3>
<u>Explanation</u></h3>
where a-term determines how wide/narrow/upward or downward of the graph.
h-term determines the changes of graph for x-axis
k-term determines the changes of graph for y-axis.
The vertex of parabola is at (h,k).
Therefore, h = 6 and k = 3.
<h3>
<u>Answer</u></h3>
<u>
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