University:
High School
Course:
High School Mathematics
Academic year:

2024
Views:

384

Pages:

3
Author:

Yosef Mcclure

Modeling with Quadratic Functions Writing Equations to Model Data When data have equally-spaced inputs, you can analyze patterns in the differences of the outputs to determine what type of function can be used to model the data. Linear data have constant.firstdifferences. Quadratic data have constant second differences. The first and second differences of/(x) = .x2 are shown below. Equally-spaced x-values A -3 X f(x) first differences: second differences: 9 -2 -1 0 l 1 0 1 4 2 -- 3 9 4 '\./\I \ I\1I\3I'\.5I -5 - 3 - 1 '\.I\/\ I\/\ I 2 2 2 2 2 EXAMPLES (Continued) 3• Eq u� o n EquCA-t1on E � uG\-ho"' Write an equation of the parabola that passes through the points (- l, 41)� (0, 1) and , 7) Q 2 + b ;x. + C =-'I, I : Q (- 1 \'2. + b { -1 -+ c. :. - b -+ c. = ==> 2: °'(0)1..+b&"o)+c-=l => 0 3: a( (2.)£1 E3 '). �) + b(2.) -+ c.=- 1i 2a-2 4ll + UJC\ li>a + li> ti\ loo. � °' t.!i 1 +2.C=I? b + C == 7 + 3G = 15 ⇒ E: 4ai + 26 + c =- 7 1'1u5 in a=2 e1nd c•\ i<'--tO E\ I E2 I or E3 anJ So\ve. -fur 2.-b+\ -= 4 3-b = 4 3 ( 1 ) = IS -3 + 3 = IS - --b: I -3 - j =- 12... � c.=- 4 3 � \NY ;'le. 't\,,e, e.q uwn 01') of +\..e.. pa.ra be\ a. +(x)� \ -i:(x) xi + x�c = 2x2. - X + \] b.