Question 31796
SEE MY COMMENTS BELOW..AND THE ADDDITIONAL EXAMPLE GIVEN BELOW
Can someone help? and check my answer to see if im doing this right?
For the function y = x^2 - 4x - 5, perform the following tasks:
(1)Put the function in the form y = a(x - h)^2 + k.
I got the answer: y = (x-2)^2 - 9......................OK
What is the line of symmetry?
I got the answer: x = 2...OK..VERY GOOD
Graph the function using the equation in part (1).
 {{{ graph( 600, 600, -6, 6, -10, 10, ((x-2)^2-9),(x-2)/0.000001) }}}
 Explain why it is not necessary to plot points to graph when using y = a (x – h)^2 + k.
 YOU CAN DRAW LINE OF SYMMETRY.,PLOT VERTEX AND SKETCH THE GRAPH ON EITHER SIDE OF LINE OF SYMMETRY BY SMOOTH LINES NOTING,THE X INTERCEPTS OF -1 AND 5 AND  THAT Y TENDS TO INFINITY AS X TENDS TO INFINITY.
how does this graph compare to the graph of y = x^2?
 {{{ graph( 600, 600, -6, 6, -10, 10,((x-2)^2-9), x^2,(x-2)/0.000001) }}}

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SEE THE FOLLOWING EXAMPLE WHICH IS ALMOST SAME AS YOUR PROBLEM AND TRY.IF STILL IN DIFFICULTY PLEASE COME BACK.
Y=X^2-2X-3=X^2-2*X*1+1^2-1-3=(X-1)^2-1-3=(X-1)^2-4=0
X INTERCEPT IS OBTAINED BY PUTTING Y=0....WE GET
X^2-2X-3=0=X^2-3X+X-3=X(X-3)+1(X-3)=(X-3)(X+1)=0...SO..X=3 OR -1...
Y INTERCEPT IS GOT BY PUTTING X =0...WE GET
Y=0-0-3=-3
SEE THE GRAPH BELOW ......
graph( 500, 500, -10, 20, -20, 20,x^2-2x-3 )
THE AXIS IS X=1 AS YOU CAN SEE FROM THE GRAPH
ONE POINT SYMMETRIC TO Y INTERCEPT??NO...SYMMETRIC TO AXIS IT IS......(-1,3)
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I have to put this equation y=x^2-2x-15 into this form y=a(x-h)^2+k.
MAKE A PERFECT SQUARE USING X^2 AND X TERMS.ADD AND SUBTRACT THE REQUIRED CONSTANT FOR THE PURPOSE.
Y=(X-1)^2-1-15=(X-1)^2-16...COMPARING WITH THE ABOVE
y=a(x-h)^2+k.
WE GET A=1 AND K=-16
I have to find the line of symmetry.
X-1=0 IS THE LINE OF SYMMETRY SINCE ON EITHER SIDE OF X=1,WE GET SYMMETRIC/SAME VALUES FOR Y..AT X=1+2=3..Y IS -12 AND AT X=1-2=-1 ALSO WE GET Y=-12
(h,k)=vertex I think you use complete the square technique.
YA ..THE VERTEX AS YOU SHOULD KNOW NOW IS AT X=1 AND AT X=1 ,Y=-16 .SO (1,-16) IS THE VERTEX
THE GRAPH WILL LOOK LIKE THIS
graph( 500, 500, -10, 20, -20, 20, x^2-2x-15 )
Please help. thanks