What is the focus of the parabola y = -10x^2? Simplify any fractions. (______,______)

Identify Orientation: Identify the orientation of the parabola. Since the equation is y = -10x^2, it's a vertical parabola.Find Values: Find the values of a, h, and k from the equation y = -10x^2. Comparing with y = a(x - h)^2 + k, we get a = -10, h = 0, and k = 0.Calculate p: Calculate the value of p using the formula p = 1/(4a). p = 1/(4*(-10)) = -1/40.Determine Focus: Determine the focus of the parabola using the values of h, k, and p. The focus is at (h, k + p), so it's (0, 0 - 1/40) which simplifies to (0, -1/40).

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What is the focus of the parabola $y = -10x^2$ ? $\newline$ 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 = -10x^2

\newline

Simplify any fractions.

\newline

(______,______)

Identify Orientation: Identify the orientation of the parabola. Since the equation is $y = -10x^2$ , it's a vertical parabola.
Find Values: Find the values of $a$ , $h$ , and $k$ from the equation $y = -10x^2$ . $\newline$ Comparing with $y = a(x - h)^2 + k$ , we get $a = -10$ , $h = 0$ , and $k = 0$ .
Calculate $p$ : Calculate the value of $p$ using the formula $p = \frac{1}{4a}$ . $p = \frac{1}{4(-10)} = -\frac{1}{40}$ .
Determine Focus: Determine the focus of the parabola using the values of $h$ , $k$ , and $p$ . The focus is at $(h, k + p)$ , so it's $(0, 0 - \frac{1}{40})$ which simplifies to $(0, -\frac{1}{40})$ .