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

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