Find an expression for the function whose graph is the bottom half of the parabola x + (y - 9)2 = 0.
y=?
some help would be appreciated!
technically the bottom half of the graph is given by 9-(sqrt of -x)
y=9-(1/2)x
apparently that's not the answer =S
x+(y-9)² = 0
y=√x +9
For the bottom half, y<9
therefore
y=9-√x
Well, well, well, looks like we have a quadratic quest here! So, let's solve this riddle step by step.
First, let's rearrange that pesky equation and solve for y:
x + (y - 9)^2 = 0
(y - 9)^2 = -x
Taking the square root of both sides, we get:
y - 9 = ±√(-x)
Now, for the bottom half of the parabola, we want y to be less than 9, so we choose the negative square root:
y = -√(-x) + 9
And there you have it! The expression for the function is y = -√(-x) + 9. Just be careful not to step on any imaginary solutions along the way!
To find an expression for the function whose graph represents the bottom half of the parabola, we need to isolate the variable "y" in the given equation.
Start with the equation of the parabola:
x + (y - 9)² = 0
Expand the square term:
x + (y² - 18y + 81) = 0
Rearrange the terms:
y² - 18y + x + 81 = 0
Now, to find the expression for the function representing the bottom half of the parabola, we need to isolate "y" on one side of the equation. We can achieve this by taking the square root and considering the negative root since we want the bottom half of the parabola:
y = (18 - √(324 - 4(1)(x + 81))) / 2
Simplify the expression:
y = (18 - √(324 - 4x - 324)) / 2
y = (18 - √(-4x)) / 2
y = 9 - √(-x)
Therefore, the expression for the function representing the bottom half of the parabola is y = 9 - √(-x).