# What are the vertex, focus, and directrix of # y=-x^2+7x+5#?

##### 1 Answer

Oct 7, 2017

Vertex

Focus

Directrix

#### Explanation:

Given -

#y=-x^2+7x+5#

This parabola opens down because it is in the form

#(x-h)^2=-4a(y-k)#

Let us convert the given equation in this form

#-x^2+7x+5=y#

#-x^2+7x=y-5#

#x^2-7x=-y+5#

#x^2-7x+49/4=-y+5+49/4#

#(x-7/2)^2=-y+69/4#

#(x-7/2)^2=-1(y-69/4)#

#(x-7/2)^2=-4 xx 1/4(y-69/4)#

#a=1/4# Distance between focus and vertex and also distance between vertex and directix.

Vertex

Focus

Directrix