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- THIS IS PART 2 OF HOW TO GRAPH EQUATIONS
BY PLOTTING POINTS ON THE COORDINATE PLANE.
THE LAST TWO EXAMPLES WE GRAFTED TWO LINEAR EQUATIONS
AND NOW I'D LIKE TO TAKE A LOOK
AT A COUPLE OF EXAMPLES THAT ARE NOT LINEAR.
OKAY, SO WE LEFT OFF BY LOOKING AT THIS EXAMPLE,
EXAMPLE 1 AND EXAMPLE 2.
I'D LIKE TO TAKE A LOOK AT HOW TO GRAPH
Y = X SQUARED - 1, AGAIN, BY PLOTTING POINTS.
THE TECHNIQUE IS GOING TO BE THE SAME.
WE'RE GOING TO SUBSTITUTE X VALUES INTO THIS EQUATION
AND FIND THE CORRESPONDING Y VALUE.
WE CAN PICK ANY X VALUE THAT WE WOULD LIKE,
BUT WE DO HAVE TO PLOT THEM ON THE COORDINATE PLANE,
SO I'M GOING TO GO AHEAD AND PICK -2, -1, 0, 1, 2.
OKAY. SO LET'S TAKE A LOOK AT THE FIRST
VALUE OF X THAT WE CHOSE.
WE CHOSE -2.
WE'RE GOING TO SUBSTITUTE THAT IN FOR X.
WE HAVE -2 SQUARED - 1.
-2 SQUARED IS 4 - 1 WILL GIVE US 3.
OKAY, LET'S TAKE A LOOK AT THIS ON A GRAPHING CALCULATOR
JUST FOR A MOMENT.
WHEN YOU'RE SCORING A NEGATIVE NUMBER
YOU DO HAVE TO BE A LITTLE CAREFUL.
WE DO HAVE TO INCLUDE THE -2 IN A SET OF PARENTHESIS
TO EVALUATE -2 SQUARED PROPERLY.
SO A NEGATIVE TIMES A NEGATIVE IS POSITIVE.
NOTICE HOW IF I LEAVE OFF THE PARENTHESIS,
THE CALCULATOR ESSENTIALLY SQUARES THE +2,
THEN TAKES THE OPPOSITE, OR MAKES IT NEGATIVE.
SO WE WANT -2 SQUARED, +4.
SO BE CAREFUL ABOUT THAT
WHEN YOU'RE USING THE GRAPHING CALCULATOR.
OKAY, BACK OVER TO OUR PROBLEM.
NOW, WE'RE GOING TO SQUARE -1 AND SUBTRACT 1.
OF COURSE, YOU'RE GOING TO GET 0.
AND JUST TO SAVE A LITTLE BIT OF TIME HERE,
WHEN X IS 0, Y IS -1.
WHEN X IS 1, Y IS 0.
WHEN X IS 2, AGAIN, Y IS 3.
OKAY, SO WE HAVE 5 SETS OF ORDERED PAIRS.
I WON'T WRITE THEM OUT THIS TIME.
I'M GOING TO GO AHEAD AND PLOT THEM
AT (-2,3),(-1,0), (0,-1),(1,0),(2,3).
OBVIOUSLY, THIS IS NOT A LINEAR EQUATION.
IT'S ACTUALLY A DEGREE TWO EQUATION
AND IT RESULTS IN A SHAPE CALLED A PARABOLA,
WHICH IS KIND OF A "U" SHAPE.
ONE MORE EXAMPLE.
WE'RE GOING TO GRAPH X = Y SQUARED.
NOW, THIS EQUATION IS A LITTLE BIT DIFFERENT
THAN THE REST OF THEM
BECAUSE THE Y VARIABLE IS BEING SQUARED.
X = Y SQUARED.
SO IN THIS CASE, IT WOULD BE EASIER FOR US
TO CHOOSE VALUES OF Y, SQUARE THEM,
AND THEN GET X.
A LITTLE BIT OF CHANGE FROM THE ROUTINE.
NOW, WE COULD PICK X VALUES,
BUT IT WOULD MAKE IT MUCH MORE DIFFICULT
TO FIND THE CORRESPONDING Y VALUES.
OKAY, SO ESSENTIALLY,
IN ORDER TO FIND THE VALUE OF X
WE JUST HAVE TO SQUARE Y.
SO IF I SQUARE -2, I HAVE 4, AND SO ON.
AGAIN, YOU CAN WRITE THESE AS ORDERED PAIRS,
BUT WE KIND OF GET THE IDEA FROM THE LAST VIDEO.
LET'S GO AHEAD AND PLOT THESE POINTS
(+4,-2),(+1,-1),(0,0) THE ORIGIN, (1,1) AND (4,2).
AND AGAIN, IT'S NOT A LINEAR EQUATION.
AND YOU CAN SEE IT ALMOST LOOKS LIKE
A PARABOLA TURNED ON ITS SIDE.
OKAY. I HOPE IT HELPS YOU REVIEW
HOW TO GRAPH EQUATIONS BY PLOTTING POINTS.
REMEMBER EACH POINT REPRESENTS ONE SOLUTION FOR THE EQUATION
AND ALL OF THESE EQUATIONS THAT WE'VE DONE,
THERE'S AN INFINITE NUMBER OF SOLUTIONS.
WE JUST PICK ENOUGH
SO YOU CAN MAKE A NICE GRAPH OF THE EQUATION.
I'LL LEAVE YOU WITH A THOUGHT
AND I HOPE THAT HELPS YOU UNDERSTAND
HOW TO GRAPH EQUATIONS BY PLOTTING POINTS.