Question

The equation of a parabola is given. y=18x2+4x+20 What are the coordinates of the focus of the parabola?

Answer 1

The equation of a parabola is given. y=$18x^2+4x+20$

Here the value of 'a' = 18 and it is positive, it means the parabola opens up.

For vertical parabola the focus point is (h , k+p)

Where (h,k) is the vertex and p = $\frac{1}{4a}$ (p is the distance between vertex and focus)

First we find vertex (h,k)

h = $\frac{-b}{2a}$

a = 18 and b = 4

So h= $\frac{-4}{2*18}$ = $\frac{-4}{36}$ = $\frac{-1}{9}$

Plug in -1/9 for x and find out k

k = $y = 18x^2+4x+20 = 18(\frac{-1}{9})^2 + 4(\frac{-1}{9}) + 20$

= $(\frac{2}{9}) + (\frac{-4}{9}) + 20$

= $\frac{178}{9}$

So vertex is ($\frac{-1}{9}$, $\frac{178}{9}$)

P = $\frac{1}{4a}$, we know a= 18

So p = $\frac{1}{4*18}$ = $\frac{1}{72}$

Focus is ( h, k +p)

h = $\frac{-1}{9}$ k = $\frac{178}{9}$

and p = $\frac{1}{72}$

k + P = $\frac{178}{9}$ + $\frac{1}{72}$

Take common denominator 72

k + p = $\frac{1424}{72}$ + $\frac{1}{72}$ = $\frac{1425}{72}$ = $\frac{475}{24}$

Focus point is ( $\frac{-1}{9}$ , $\frac{475}{24}$)

Answer 2

Answer:

(-16,-10)

Step-by-step explanation:

I took the test. The other answer is wrong because you pasted it incorrectly.