What is the focus of the parabola y = -3x^2? Simplify any fractions. (______,______)

Identify Parabola Orientation: Identify the orientation of the parabola. Since the equation is y = -3x^2, it's a vertical parabola.Find Values of a, h, k: Find the values of a, h, and k. The equation y = -3x^2 can be rewritten as y = -3(x - 0)^2 + 0. So, a = -3, h = 0, and k = 0.Calculate Value of p: Calculate the value of p using the formula p = 1/(4a). p = 1/(4*(-3)) p = -1/12Determine Parabola Focus: Determine the focus of the parabola using the values of h, k, and p. The focus is at (h, k + p). So, the focus is at (0, 0 + (-1/12)).Write Focus Coordinates: Write the coordinates of the focus. The focus of the parabola is (0, -1/12).

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What is the focus of the parabola $y = -3x^2$ ? $\newline$ Simplify any fractions. $\newline$ (,)

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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 = -3x^2

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Simplify any fractions.

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(______,______)

Identify Parabola Orientation: Identify the orientation of the parabola. $\newline$ Since the equation is $y = -3x^2$ , it's a vertical parabola.
Find Values of $a$ , $h$ , $k$ : Find the values of $a$ , $h$ , and $k$ . The equation $y = -3x^2$ can be rewritten as $y = -3(x - 0)^2 + 0$ . So, $a = -3$ , $h = 0$ , and $h$ $0$ .
Calculate Value of p: Calculate the value of $p$ using the formula $p = \frac{1}{4a}$ . $p = \frac{1}{4(-3)}$ $p = -\frac{1}{12}$
Determine Parabola Focus: Determine the focus of the parabola using the values of $h$ , $k$ , and $p$ . The focus is at $(h, k + p)$ . So, the focus is at $(0, 0 + (-\frac{1}{12}))$ .
Write Focus Coordinates: Write the coordinates of the focus. $\newline$ The focus of the parabola is $(0, -\frac{1}{12})$ .