Given the vertex of a parabola is (-6, 8) and its focus is (-6, 10), find the equation.

Step-by-step explanation:

If you plot the vertex and the focus, you'll see that the focus is 2 units above the vertex. That tells us 2 things: first, that the parabola opens upwards and, second, that the value of p in our equation is 2 (since p is the number of units between the vertex and the focus). The equation is:

where h and k are the coordinates of the vertex and p is the number of units between the vertex and the focus. The vertex is given as (-6, 8), so h is -6 and k is 8. p is 2, so filling in we get:

which simplifies down to

Not sure in what form you need it, so I'll leave it like that and you may have to do some algebraic manipulation to get it into the form your teacher wants it in.

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225