Find axis of symmetry and vertex of x=5y220y+23?

1 Answer
Nov 14, 2017

AXIS OF SYMMETRY: y=2
VERTEX: (3,2)

Explanation:

STANDARD FORM: x=ay2+by+c
AXIS OF SYMMETRY: y=b2a
REFERENCE STANDARD FORM TO FIND a,b,c, THEN FIND y=b2a.
y=(20)2(5)=2010=2
y=2

VERTEX FORM: x=a(yk)2+h
VERTEX: (h,k)
PUT INTO VERTEX FORM, THEN FIND (h,k).
x=5y220y+23 [Subtract constant.]
x23=5y220y [Factor to isolate y2.]
x23=5(y24y) [Complete the square.]
x23+5(4)=5(y24y+4) [Factor & Simplify.]
x3=5(y2)2 [Isolate x.]
x=5(y2)2+3
(h,k)=(3,2)
(3,2)