What is the focus of the parabola y = –x^2? Simplify any fractions. (______,______)

Equation of the Parabola: We have the equation of the parabola: y = -x^2. This is a vertical parabola that opens downwards because the coefficient of x^2 is negative.Standard Form of a Vertical Parabola: The standard form of a vertical parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. In our case, the equation y = -x^2 can be rewritten as y = -1(x - 0)^2 + 0, which means that a = -1, h = 0, and k = 0.Calculating the Focus: The focus of a parabola is located at (h, k + p), where p is the distance from the vertex to the focus and is calculated by the formula p = 1/(4a). Since a = -1, we can calculate p as follows: p = 1/(4*(-1)) = -1/4.Finding the Focus: Now that we have p = -1/4, we can find the focus of the parabola. The focus will be at (h, k + p) = (0, 0 + (-1/4)) = (0, -1/4).

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What is the focus of the parabola $y = -x^2$ ? $\newline$ Simplify any fractions. $\newline$ (_ , _) $\newline$

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Algebra 2

Find the focus or directrix of a parabola

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Q. What is the focus of the parabola

y = -x^2

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Simplify any fractions.

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(_____ , _____)

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Equation of the Parabola: We have the equation of the parabola: $y = -x^2$ . This is a vertical parabola that opens downwards because the coefficient of $x^2$ is negative.
Standard Form of a Vertical Parabola: The standard form of a vertical parabola is $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola. In our case, the equation $y = -x^2$ can be rewritten as $y = -1(x - 0)^2 + 0$ , which means that $a = -1$ , $h = 0$ , and $k = 0$ .
Calculating the Focus: The focus of a parabola is located at $(h, k + p)$ , where $p$ is the distance from the vertex to the focus and is calculated by the formula $p = \frac{1}{4a}$ . Since $a = -1$ , we can calculate $p$ as follows: $p = \frac{1}{4(-1)} = -\frac{1}{4}$ .
Finding the Focus: Now that we have $p = -\frac{1}{4}$ , we can find the focus of the parabola. The focus will be at $(h, k + p) = (0, 0 + (-\frac{1}{4})) = (0, -\frac{1}{4})$ .