Question

(NEED HELP ASAP!!)

What are the coordinates of the focus of the parabola?


A: (8, 6)

B: (-8, 6)

C: (-8, 2)

D: (8, 2)

Answer 1

C: (-8, 2)

Explanation:

Given parabola:

`y=-(1)/(8)x^2-2x-4`

For the quadratic equation in the form y = ax² + bx + c, the x-value of the vertex is -b/2a.

Therefore, the x-value of the vertex of the given parabola is:

`\implies x=-(b)/(2a)=-(-2)/(2\left(-(1)/(8)\right))=-8`

To find the y-value of the vertex, input x = -8 into the given equation:

`\implies y=-(1)/(8)(-8)^2-2(-8)-4=4`

Therefore, the vertex (h, k) of the parabola is (-8, 4).

The focus of the parabola is (h, k+p) where:

• (h, k) is the vertex

• 
  `p=(1)/(4a)`

Therefore:

`\implies \textsf{Focus}=\left(-8,4+(1)/(4\left(-(1)/(8)\right))\right)=\left(-8,2)`