What is the focus of the parabola y = 9x^2 + 1? Simplify any fractions. (______,______)

Identify vertex form: Identify the vertex form of the parabola. y = 9x^2 + 1 is in the form y = a(x - h)^2 + k, where a = 9, h = 0, and k = 1.Calculate value of p: Calculate the value of p using the formula p = 1/(4a). p = 1/(4*9) p = 1/36Determine focus: Determine the focus of the parabola using the vertex (h, k) and the value of p. Since the parabola is vertical, the focus is (h, k + p). Focus = (0, 1 + 1/36) Focus = (0, 37/36)

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What is the focus of the parabola $y = 9x^2 + 1$ ? $\newline$ 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 = 9x^2 + 1

\newline

Simplify any fractions.

\newline

(______,______)

Identify vertex form: Identify the vertex form of the parabola. $\newline$ $y = 9x^2 + 1$ is in the form $y = a(x - h)^2 + k$ , where $a = 9$ , $h = 0$ , and $k = 1$ .
Calculate value of p: Calculate the value of p using the formula $p = \frac{1}{4a}$ . $p = \frac{1}{4\times 9}$ $p = \frac{1}{36}$
Determine focus: Determine the focus of the parabola using the vertex $(h, k)$ and the value of $p$ . Since the parabola is vertical, the focus is $(h, k + p)$ . Focus = $(0, 1 + \frac{1}{36})$ Focus = $(0, \frac{37}{36})$