Answer:
The parabola is translated down 2 units.
Step-by-step explanation:
You have the parabola f(x) = 2x² – 5x + 3
To change this parabola to f(x) = 2x² - 5x + 1, you must have performed the following calculation:
f(x) = 2x² – 5x + 3 -2= 2x² - 5x + 1 <u><em>Expresion A</em></u>
The algebraic expression of the parabola that results from translating the parabola f (x) = ax² horizontally and vertically is g (x) = a(x - p)² + q, translating in the same way as the function.
- If p> 0 and q> 0, the parabola shifts p units to the right and q units up.
- If p> 0 and q <0, the parabola shifts p units to the right and q units down.
- If p <0 and q> 0, the parabola shifts p units to the left and q units up.
- If p <0 and q <0, the parabola shifts p units to the left and q units down.
In the expression A it can be observed then that q = -2 and is less than 0. So the displacement is down 2 units.
This can also be seen graphically, in the attached image, where the red parabola corresponds to the function f(x) = 2x² – 5x + 3 and the blue one to the parabola f(x) = 2x² – 5x + 1.
In conclusion, <u><em>the parabola is translated down 2 units.</em></u>
Answer:
17 - 7m
Step-by-step explanation:
Assuming you require to subtract the expressions, then
16 + m - (8m - 1) ← distribute parenthesis by - 1
= 16 + m - 8m + 1 ← collect like terms
= 17 - 7m
We notice that the number of pages read is a function of the number of days:
If y is the # of pages read and x the # days, so the equation becomes:
y = m.x + b where m is the rate of reading or the slope and b a constant. How to calculate m? and later b
Note that we can rewrite the given as:
x| 0 | 2 | 5 | 7 |
-|------|-----|-----|------|
y| 57 | 99|162 |204 |
m= (y₂-y₁)/(x₂-x₁) = Rise/Run
m= (204-162)/(7-5) = (162-99)/(5-2) = (99-57)/(2-0) = 21
Then
m = 21 and the function y = 21.x +b
We notice in the table that when x = 0; y = 57, then
57 = 0.x + b that means b = 5 and the final equation is:
y = 21.x + 57
Step-by-step explanation:
Thus, option A > is the correct answer.