IN THIS PROBLEM WE'RE ASKED
TO FIND THE QUADRATIC FUNCTION
GIVEN THE INTERCEPTS
OF THE FUNCTION.
SO BECAUSE WE'RE GIVEN
THE INTERCEPTS
OF OUR QUADRATIC FUNCTION
WE ARE GOING TO FIRST FIND
THE FUNCTION IN FACTORED FORM
AND THEN IF WE NEED TO
WE CAN MULTIPLY IT OUT
SO THAT IT'S IN GENERAL FORM.
THE FACTORED FORM
OF A QUADRATIC FUNCTION
WITH 0s R SUB 1 AND R SUB 2
CAN BE GIVEN BY F OF X = "A"
A CONSTANT x THE FACTOR
OF X - R SUB 1
x THE FACTOR OF X - R SUB 2.
LOOKING AT OUR GRAPH NOTICE
HOW WE HAVE AN X INTERCEPT
OF -4 AND X INTERCEPT OF +3.
SO X = -4 WOULD BE A 0 OF THE
FUNCTION AND SO WOULD X = +3.
SO IF OUR FUNCTION
IN FACTORED FORM
IS IN THE FORM OF F OF X =
"A" x A  FACTOR OF X - R SUB 1
x THE FACTOR OF X - R SUB 2
WE CAN SUBSTITUTE -4 FOR R
SUB 1 AND +3 FOR R SUB 2.
SO THIS WOULD GIVE US F OF X
= "A" x X - -4 BECOMES + 4
AND X - 3.
NOW WE CAN USE THE Y INTERCEPT
TO DETERMINE THE VALUE OF "A".
IF OUR GRAPH CONTAINS
THE POINT 0, 6
THIS MEANS F OF 0 MUST = 6.
WHEN X IS 0, THE FUNCTION
VALUE OR Y MUST BE 6.
SO IF WE SUBSTITUTE 0 FOR X
THIS FUNCTION VALUE MUST BE 6.
SO F OF 0 WOULD HAVE TO BE
"A" x 0 + 4 IS 4
AND 0 - 3 IS -3
BUT THIS MUST EQUAL
THE FUNCTION VALUE OF +6
AND NOW WE CAN SOLVE FOR "A".
WE WOULD HAVE -12A = +6
DIVIDE BOTH SIDES BY -12
AND WE HAVE "A" = -1/2,
THEREFORE OUR FUNCTION
IN FACTORED FORM WOULD BE
F OF X = -1/2 x THE QUANTITY
X + 4 x THE QUANTITY X - 3.
THIS WOULD BE THE QUADRATIC
FUNCTION GRAPHED HERE
WITH THE GIVEN INTERCEPTS.
OF COURSE IF WE NEEDED TO
EXPRESS THIS IN GENERAL FORM
WE WOULD HAVE TO MULTIPLY
THIS OUT
BUT FOR THIS VIDEO I THINK
WE'LL GO AHEAD AND STOP HERE.
