Name the focus of y = 0.6x^2.

1 answer:

4 0

Parabola
remember that
parabola equation is
4p(y-k) =(x-h)^2 for a verticl parabola
p=distance from vertex to focus and from vertex to directix
solve for p, k, h

y=0.6x^2

4p(y-0)=(x-0)^2
divide both sides by 4p
(y-0)=1/4p times (x-0)^2
y=0.6x^2

1/(4p)=0.6
find p
multiply 4p
1=2.4p
divide 2.4
1/2.4=p
h=0,k=0
vertex=0,0
opens up so go up to find focus
(0,0)
0+1/2.4=1/2.4
focus is at (0,1/2.4)

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General Formulas and Concepts:

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Limits

Right-Side Limit: $\displaystyle \lim_{x \to c^+} f(x)$
Left-Side Limit: $\displaystyle \lim_{x \to c^-} f(x)$

Limit Rule [Variable Direct Substitution]: $\displaystyle \lim_{x \to c} x = c$

Limit Property [Addition/Subtraction]: $\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)$

Step-by-step explanation:

*Note:

In order for a limit to exist, the right-side and left-side limits must equal each other.

Step 1: Define

Identify

$\displaystyle f(x) = \left\{\begin{array}{ccc}5 - x,\ x < 5\\8,\ x = 5\\x + 3,\ x > 5\end{array}$

Step 2: Find Right-Side Limit

Substitute in function [Limit]: $\displaystyle \lim_{x \to 5^+} 5 - x$
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Step 3: Find Left-Side Limit

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