Answer:
The vertex is y=-4
Step-by-step explanation:
The vertex is the minimum point of the graph of the quadratic equation.
Let's first find the like of symmetry.
dy/dx=2x+12
2x+12=0
2x=-12
x=-6
Now plug -6 into the quadratic equation
y=(-6)²+12(-6)+32
y=-4
Answer:
(2, 2, 1)
Step-by-step explanation:
You can see that the point is moved 2 units (x axis), 2 units (y axis) and 1 unit (z axis). Because you write coordiantes as (x,y,z), you write (2,2,1)
Take the second equation and flip it around so the y on the left ends up on the right and the 4x on the right ends up on the left. This makes all negatives positive and all positives negative. -4x + 12 = y
Then add the first equation to the second equation
4x +12 = -7y
<u>-4x + 12 </u>=<u> y </u> this eliminates the x's
<u>24</u> = -<u> 6y</u> then divide by - 6
- 6 - 6
- 4 = y<u>
</u>So if you know that y = negative 4, you can substitute into either equation. I pick the second one because I am a lazy person.
-y + 12 = 4 x
-(-4) + 12 = 4 x combine your numbers<u>
</u> <u> 16 </u> = <u>4 x </u> then divide by 4<u>
</u> 4 = x
So your solution is: x = 4 and y = -4 or this is also written (4, -4)
Does that work for you?
Answer:
Yes . You are correct.
Step-by-step explanation:
(x + 5)^2 + (y + 10)^2 = 81.
2 times 108 is 216
3 times 72 is 216
4 times 54 is 216
6 times 36 is 216
