QuestionFind the formula for the bottom half of the parabola defined by $x + (y - 9)^{2} = 0$ . What is $y=$ ?

Studdy Solution

STEP 1

Assumptions1. The given equation is a parabola $x+(y-9)^{}=0$ . We are looking for the function that represents the bottom half of this parabola.

STEP 2

The given equation is in the form of a parabola $x = -(y-k)^2 + h$ , where $(h,k)$ is the vertex of the parabola. In this case, the vertex is at $(0,9)$ .

STEP 3

We can rewrite the given equation in terms of $y$ to get the function.
$y =9 - \sqrt{-x}$

STEP 4

However, this is the equation for the entire parabola. Since we only want the bottom half, we need to restrict the domain of the function. The bottom half of the parabola is when $y$ is less than or equal to the $y$ -coordinate of the vertex, which is $9$ .

STEP 5

Therefore, the function representing the bottom half of the parabola is $y =9 - \sqrt{-x}, \quad \text{for } y \leq9$

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QuestionFind the formula for the bottom half of the parabola defined by $x + (y - 9)^{2} = 0$ . What is $y=$ ?

Studdy Solution

STEP 1

Assumptions1. The given equation is a parabola $x+(y-9)^{}=0$ . We are looking for the function that represents the bottom half of this parabola.

STEP 2

The given equation is in the form of a parabola $x = -(y-k)^2 + h$ , where $(h,k)$ is the vertex of the parabola. In this case, the vertex is at $(0,9)$ .

STEP 3

We can rewrite the given equation in terms of $y$ to get the function.
$y =9 - \sqrt{-x}$

STEP 4

However, this is the equation for the entire parabola. Since we only want the bottom half, we need to restrict the domain of the function. The bottom half of the parabola is when $y$ is less than or equal to the $y$ -coordinate of the vertex, which is $9$ .

STEP 5

Therefore, the function representing the bottom half of the parabola is $y =9 - \sqrt{-x}, \quad \text{for } y \leq9$

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QuestionFind the formula for the bottom half of the parabola defined by x+(y−9)2=0x + (y - 9)^{2} = 0x+(y−9)2=0. What is y=y=y=?

Studdy Solution

STEP 1

Assumptions1. The given equation is a parabola x+(y−9)=0x+(y-9)^{}=0x+(y−9)=0 . We are looking for the function that represents the bottom half of this parabola.

STEP 2

The given equation is in the form of a parabola x=−(y−k)2+hx = -(y-k)^2 + hx=−(y−k)2+h, where (h,k)(h,k)(h,k) is the vertex of the parabola. In this case, the vertex is at (0,9)(0,9)(0,9).

STEP 3

We can rewrite the given equation in terms of yyy to get the function.y=9−−xy =9 - \sqrt{-x}y=9−−x​

STEP 4

However, this is the equation for the entire parabola. Since we only want the bottom half, we need to restrict the domain of the function. The bottom half of the parabola is when yyy is less than or equal to the yyy-coordinate of the vertex, which is 999.

STEP 5

Therefore, the function representing the bottom half of the parabola isy=9−−x,for y≤9y =9 - \sqrt{-x}, \quad \text{for } y \leq9y=9−−x​,for y≤9

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QuestionFind the formula for the bottom half of the parabola defined by $x + (y - 9)^{2} = 0$ . What is $y=$ ?

Assumptions1. The given equation is a parabola $x+(y-9)^{}=0$ . We are looking for the function that represents the bottom half of this parabola.

The given equation is in the form of a parabola $x = -(y-k)^2 + h$ , where $(h,k)$ is the vertex of the parabola. In this case, the vertex is at $(0,9)$ .

We can rewrite the given equation in terms of $y$ to get the function.
$y =9 - \sqrt{-x}$

However, this is the equation for the entire parabola. Since we only want the bottom half, we need to restrict the domain of the function. The bottom half of the parabola is when $y$ is less than or equal to the $y$ -coordinate of the vertex, which is $9$ .

Therefore, the function representing the bottom half of the parabola is $y =9 - \sqrt{-x}, \quad \text{for } y \leq9$