Question 31796: 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
What is the line of symmetry?
I got the answer: x = 2
Graph the function using the equation in part (1). Explain why it is not necessary to plot points to graph when using y = a (x – h)^2 + k.
how does this graph compare to the graph of y = x^2?
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! 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).
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?
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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
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