1. Consider y=f(x)
2. let a and b be 2 positive numbers
3. then the graph of y=f(x)-a is the graph of y=f(x) shifted a units down
4. the graph of y=f(x+b) is y=f(x) shifted b units left
y=f(x-b) is y=f(x) shifted b units right
5. y=f(x+b)-a is the graph of y=f(x) shifted a units down and b units left
6. So
shifted 4 units down and 5 units left is the graph of
7. To check: consider
at x=3. We have the point (3, 27)
Shift this point 4 units down and 5 units left: (3-5, 27-4)=(-2, 23)
Consider
for x=-2
Answer:
Step-by-step explanation:
In order for the polynomial to be a degree of 4, it must have exactly 4 roots. According to the fundamental theorem of algebra: "The number of roots in a function is equivalent to the degree of the function"
These roots do not have to be real numbers, which means they can be imaginary or complex.
In this case, (-11 - √2i), (3 + 4i), and 10. There are three roots, which means that the polynomial can be a third of fourth degree polynomial. It is wrong for Patricia to assume that this is a fourth degree polynomial when only three roots are known.
<h3><u>The degree of the polynomial will at least be three, but could be higher.</u></h3>
Answer:
24:12:28:12
Step-by-step explanation:
76÷19=4
6×4:3×4:7×4:3×4
=24:12:28:12
EC= 12sqrt2
Use the pythagorean theorem to find EC.
6^2+EC^2=18^2
36+EC^2=324
EC^2=288
square root both sides
EC= 12sqrt2