What is the focus of the parabola y = 6x^2 + 3? Simplify any fractions. (______,______)

Identify Vertex Form: Identify the vertex form of the parabola. The given equation y = 6x^2 + 3 is already in the form y = a(x - h)^2 + k, where a = 6, h = 0, and k = 3.Calculate p Value: Calculate the value of p using the formula p = 1/(4a). p = 1/(4*6) p = 1/24Determine Focus: Determine the focus of the parabola. The focus is at (h, k + p) since the parabola opens upwards. Focus = (0, 3 + 1/24) Focus = (0, 3 + 0.0416667)Simplify Focus Coordinates: Simplify the focus coordinates. Focus = (0, 3.0416667) Since we need to simplify any fractions, we'll keep the fraction form for the y-coordinate. Focus = (0, 73/24)

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What is the focus of the parabola $y = 6x^2 + 3$ ? $\newline$ 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 = 6x^2 + 3

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Simplify any fractions.

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(______,______)

Identify Vertex Form: Identify the vertex form of the parabola. $\newline$ The given equation $y = 6x^2 + 3$ is already in the form $y = a(x - h)^2 + k$ , where $a = 6$ , $h = 0$ , and $k = 3$ .
Calculate p Value: Calculate the value of p using the formula $p = \frac{1}{4a}$ . $p = \frac{1}{4\times 6}$ $p = \frac{1}{24}$
Determine Focus: Determine the focus of the parabola. $\newline$ The focus is at $(h, k + p)$ since the parabola opens upwards. $\newline$ Focus $= (0, 3 + \frac{1}{24})$ $\newline$ Focus $= (0, 3 + 0.0416667)$
Simplify Focus Coordinates: Simplify the focus coordinates. $\newline$ Focus = $(0, 3.0416667)$ $\newline$ Since we need to simplify any fractions, we'll keep the fraction form for the y-coordinate. $\newline$ Focus = $(0, \frac{73}{24})$