Because the vertex of the parabola is at (16,0), its equation is of the formy = a(x-10)² + 15
The graph goes through (0,0), thereforea(0 - 10)² + 15 = 0100a = -15a = -0.15
The equation is y = f(x) = -0.15(x - 10)² + 15
The graph is shown below.
Part A
Note that y = f(x).
The x-intercepts identify values where the function or y=0. The x-intercepts occur at x=0 and x=20, or at (0,0) and (20,0).
The maximum value of y occurs at the vertex (10, 15) because the curve is down due to the negative leading coefficient of -0.15.
The curve increases in the interval x = (-∞, 10) and it decreases in the interval x = (10, ∞).
Part B
When x=12, y = -0.15(12 - 10)² + 15 = 14.4When x=15, y = -0.15(15 - 10)² + 15 = 11.25
The average rate of change between x =12 to x = 15 is(11.25 - 14.4)/(15 - 12) = -1.05
This rate of change represents the slope of the secant line from A to B. It approximates the rate at which f(x) decreases in the interval x =[12, 15].
Answer: y=6^x-3
It is a exponent form of graph, so first:
y=a^x-b
When b=0, the asymptote is y=0 but as the asymptote given is y=-3, b=-3
Second:
the y value increases 6, when x changes 0 to 1, so a=6
Answer:
Step-by-step explanation:
(7/12) of 840 attended the concert:
(7/12)*(840) = 490 students attended the Spring Concert.
(840 - 490) = 350 did not attend
(350/840) is the fraction of students who did not attend. This can be reduced to (35/84)
(350/840) = 0.4167 or 41.67% did not attend.
Let S be the amount in a savings account.
Let m be the number of months.
General equation
S = 132 + 27m
Specific question
July is the 7th month of the year including both January and July.
S = 132 + 7*27
S = 132 + 189
S = 321
Reasonableness?
Good question. You could estimate an answer.
Start with 150 dollars and say that you add 25 a month.
7 * 25 = 175
S = 150 + 175 = 325 All of this was done in my head. Since the exact answer obtained using the formula is 321, I think that's pretty reasonable using my estimate is a guide.
