What is the focus of the parabola y = 4x^2? Simplify any fractions. (______,______)

Identify Orientation: Identify the orientation of the parabola. Since the equation is y = 4x^2, it's a vertical parabola.Write in Vertex Form: Write the equation in vertex form to find a, h, and k. The equation y = 4x^2 is already in the form y = a(x - h)^2 + k with a = 4, h = 0, and k = 0.Calculate Value of p: Calculate the value of p using the formula p = 1/(4a). p = 1/(4*4) p = 1/16Find the Focus: Find the focus using the values of h, k, and p. The focus is at (h, k + p) which is (0, 0 + 1/16).

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What is the focus of the parabola $y = 4x^2$ ? $\newline$ 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 = 4x^2

\newline

Simplify any fractions.

\newline

(______,______)

Identify Orientation: Identify the orientation of the parabola. $\newline$ Since the equation is $y = 4x^2$ , it's a vertical parabola.
Write in Vertex Form: Write the equation in vertex form to find $a$ , $h$ , and $k$ . The equation $y = 4x^2$ is already in the form $y = a(x - h)^2 + k$ with $a = 4$ , $h = 0$ , and $k = 0$ .
Calculate Value of p: Calculate the value of p using the formula $p = \frac{1}{4a}$ . $\newline$ $p = \frac{1}{4\times 4}$ $\newline$ $p = \frac{1}{16}$
Find the Focus: Find the focus using the values of $h$ , $k$ , and $p$ . The focus is at $(h, k + p)$ which is $(0, 0 + \frac{1}{16})$ .