Question

What is the focus of the parabola?

y = −14x² − 2x − 2

Enter your answer in the boxes.

(___, ___)

Answer 1

we have that
y = −14x² − 2x − 2

First, we need to transform the equation into its vertex form
(x - h)²=4p(y - k)
Group terms that contain the same variable
y = (−14x² − 2x )− 2
Factor the leading coefficient
y = -14*(x² + (2/14)x )− 2
Complete the square Remember to balance the equation
y = -14*(x² + (2/14)x +(2/28)²-(2/28)²)− 2
y = -14*(x² + (2/14)x +(2/28)²)− 2+14*(2/28)²
y = -14*(x² + (2/14)x +(2/28)²)− 2+56/784
Rewrite as perfect squaresy = -14*(x+(2/28))²− 1512/784------>(x+1/14)²=(-1/14)*(y+1512/784)
4p=-1/14------> p=-1/56
This is a vertical parabola and its focus (h, k + p)h=-1/14k+p=(-1512/784)+(-1/56)----> (-1512-14)/784)----> -1526/784
the focus is(-1/14,-1526/784)