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What is the focus of the parabola $y = 8x^2 + 4$ ? $\newline$ Simplify any fractions. $\newline$ (,)

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Find the focus or directrix of a parabola

Full solution

Q. What is the focus of the parabola

y = 8x^2 + 4

?

\newline

Simplify any fractions.

\newline

(______,______)

Identify Parabola Type: We have $y = 8x^2 + 4$ . $\newline$ This is a vertical parabola.
Standard Form Parameters: The standard form of a vertical parabola is $y = a(x - h)^2 + k$ . Here, $a = 8$ , $h = 0$ , and $k = 4$ .
Calculate p Value: To find the focus, we need the value of $p$ , where $p = \frac{1}{4a}$ . So, $p = \frac{1}{4 \times 8}$ .
Find Focus Coordinates: Calculating $p$ gives us $p = \frac{1}{32}$ .
Calculate Focus Coordinates: The focus of a vertical parabola is at $(h, k + p)$ . So, the focus is at $(0, 4 + \frac{1}{32})$ .
Verify Calculation: Adding $4$ and $\frac{1}{32}$ , we get the focus at $(0, 4 + \frac{1}{32})$ . $\newline$ But wait, we need to add $4$ and $\frac{1}{32}$ correctly.

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