Question

What are the vertex, focus and directrix of `y=x^2-8x+7`?

Answer 1

Vertex `(4,-9)` Focus `(4,-35/4)` and directrix `y = - 37/4`

Explanation:

`y=(x^2-8x+16)-16+7 = (x-4)^2 -9` Vertex is at `(4,-9)` Vertex is at equidistant from focus and directrix. d(distance) `= 1/4|a| = 1/(4*1)=1/4` Here a =1 comparing withe general equation `y=a(x-h)^2+k` so focus co-ordinate is at`(4,(-9+1/4))=(4, -35/4)` and directrix equation is `y=-9-1/4 or y=-37/4)` graph{x^2-8x+7 [-20, 20, -10, 10]}[Ans]