We will have the following:
*First: We determine the translation rule:
We have that the point went from (3, -4) to (0, -5), thus the translation rule would be:
Second: We apply the translation rule to the other point to determine it's image, that is:
So, the image of the second point is (5, 6).
We know that
case a)the equation of the vertical parabola write in vertex form is
y=a(x-h)²+k,
where (h, k) is the vertex.
Using our vertex, we have:
y=a(x-2)²-1
We know that the parabola goes through (5, 0),
so
we can use these coordinates to find the value of a:
0=a(5-2)²-1
0=a(3)²-1
0=9a-1
Add 1 to both sides:
0+1=9a-1+1
1=9a
Divide both sides by 9:
1/9 = 9a/9
1/9 = a
y=(1/9)(x-2)²-1
the answer isa=1/9case b)the equation of the horizontal parabola write in vertex form is
x=a(y-k)²+h,
where (h, k) is the vertex.
Using our vertex, we have:
x=a(y+1)²+2,
We know that the parabola goes through (5, 0),
so
we can use these coordinates to find the value of a:
5=a(0+1)²+2
5=a+2
a=5-2
a=3
x=3(y+1)²+2
the answer isa=3
see the attached figure
Answer:
x>6
Step-by-step explanation:
2x > 16-4
x > 12/2
x > 6
Answer:
Infinite Solutions
Step-by-step explanation:
x + 2y = 10
6y = 3x - 30
To solve for x and y we use substitution method
Let's solve the first equation for x
x + 2y = 10
Subtract 2y on both sides
x = 10 - 2y
Now plug in x in second equation
6y = -3x + -30
6y = -3 (10-2y) - 30
6y = -30 + 6y - 30
6y = 6y
Both sides are the same, so both x and y have infinite solutions.
