University:
High School
Course:
High School Functions
Academic year:

2024
Views:

460

Pages:

4
Author:

J. Anderson

[1.6] QUADRTICS - ROOTSEXAMPLE #1: DETERMINE THE EXACT EQUATION OF A QUADRATIC FUNCTIONFind the equation of the quadratic function with the given zeros = x-intercepts = roots andthe point on the graph (POG). Express you answer in standard form.a. 2 and -3 with point (0,3)r=2,5=-3 (x,y)==(0,3)opposite3 = =operationEquation - -F.F.3= a(-2)(-3)=fux===((x-2)(x43)3=-69F.F. S.F.3=a-6F(x)= (x-2)(x)s) FOIL,usa==12f(x) = 12(x2-2x43x-6)- 6)S.F.f(x) -1x2-1x+3+-0.5 3.125)(0.3)2(-3.0)-4-20(2.0)1 [1.6] QUADRTICS - ROOTSb. Double zero and x = 0 with point (3, 10)(x,y)=(3,10)F(x) )=a(x+2)2 ==x-2 1x72=0X-210=a(3+2) = a 210= a (5)2F.F.S.F.10 = 25aas 2/5fex) = 0.4(x+2)2=a=0.4for = 0.4 (x+2) (x+2)20Equation F.F.fixi-0 4(x2++2xt2xt4)=F(x) = 0.4(x+2)2for = 0.4(x +4x+ 4)for=0.4x 2+ 1.6x+1.6S.F.+f(x)=0.Ax2+1.6x+1.62(0.1.6)420(-2.0)2 [1.6] QUADRTICS - ROOTSc.3+5and 3-5 - with point (2,-12) (= 3+vs, S=3-V5, (x,y)=(2,-12)for. a (x-r)(x-s)fex)= a (x- - (3+v5) ][x-(3-25)]fex= a (x-3+) (x-3+v5)(a-b) (a+b)= a2-b2aEquation->F.F.f(x)= = a[(x2-6xt9)- (ST]for==(3(x2-6x+4)fix)= a [ x2_6x+4]F.F.S.F.(2,-12) SubIN NOWfex) = =3(x-6x+4)-12 = a ((2)2- 6(2)+4)fcol=3x2-18x+1212 = Aa=4-Aa=3(0.764.0)(5.236, o)3 [1.6] QUADRTICS - ROOTSEXAMPLE #2: QUADRATICS & TUNNELSThe parabolic opening of a tunnel is 32 meters wide measured from side to side along theground. At the points that are 4 meters from each side, the tunnel entrance is 6 meters high.a. Determine the equation of the function.V=(0,13.7)fex) = a(x-16) - (x+16)(12,6)(-12,6)=x-intx-int = (0.16)= (0,-16) and 04/16m16m16-4=1232 mb. Calculate the max heigne of the tunnel, to the nearest tenth of a meter.r=16,5=-16, (x,y) =) (12,6)f(x)=a(x-r)(x-s)6 = a ( 12 - 16 ) (12+16)6= -11/2a -Equation F.F.-112 - 1/2a==f(x)== (x-16)(x+16)5656x/h= 16+(-16) = 0Height oF Tunnel2fex) = -3 (x-16) (x+16)Max height will56f(o) = -3 (0-16) (0+16)occur 1/2 waybetween x-int's56-3 (-16)(16)oo The Max height=of tunnel is56=13.71V=(0,13.7)13.7meters