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

Vertical Parabola: y = x^2 is a vertical parabola, so it opens upwards.Standard Form: The standard form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex.Calculate Parameters: For y = x^2, a = 1, h = 0, and k = 0, since it's already in the form y = (x - 0)^2 + 0.Focus Calculation: The focus of a parabola is (h, k + p), where p = 1/(4a).Calculate p: Calculate p: p = 1/(4*1) = 1/4.Substitute Values: Substitute h = 0, k = 0, and p = 1/4 into the focus formula: Focus = (0, 0 + 1/4).Focus of Parabola: The focus of the parabola y = x^2 is (0, 1/4).

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

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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 = x^2

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Simplify any fractions.

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(\_,\_

)

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Vertical Parabola: $y = x^2$ is a vertical parabola, so it opens upwards.
Standard Form: The standard form of a parabola is $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex.
Calculate Parameters: For $y = x^2$ , $a = 1$ , $h = 0$ , and $k = 0$ , since it's already in the form $y = (x - 0)^2 + 0$ .
Focus Calculation: The focus of a parabola is $(h, k + p)$ , where $p = \frac{1}{4a}$ .
Calculate $p$ : Calculate $p$ : $p = \frac{1}{4\times 1} = \frac{1}{4}$ .
Substitute Values: Substitute $h = 0$ , $k = 0$ , and $p = \frac{1}{4}$ into the focus formula: Focus = $(0, 0 + \frac{1}{4})$ .
Focus of Parabola: The focus of the parabola $y = x^2$ is $(0, \frac{1}{4})$ .