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

2024
Views:

275

Pages:

4
Author:

J. Anderson

1.7 Solve Linear-Quadratic Systems - WorksheetMCR3UlensenSOLUTIONS1) Determine if each quadratic function will intersect once, twice, or not at all with the given linearfunction.y=2x2-2x+1 andy=3x-5 -)y=-x2+3x-5andy=-x-13x-5 : 2x3-2xt10=2x2-5x+6=-23=008 They DON'T intersect8 1 POIc)y=;x?+4x-2amdy=x43d)y=->x2+++ and y=x=19=8So 2 POI's.2 POI's2) Determine the coordinates of the point(s) of intersection of each linear-quadratic system.a) y=x2-7x+15 andy=2x 5POI #1POI #2f(x) =2x-sF(x)=2x-sF(4)=2(4).5F(5)=a(s) - s0=(x-4)(x-5)F(4) : 3F(s)=5(4,3)(5,5)1:4 x = 5 b) =3x2-16x+37 andy=8x+ 18241-332-166+37POI#1POI#20= 3xa-24x+36F(x) = 8x+)f(x)=8x4)0:3(x"-8x+12)F(2)=8(2)+1F(6)=8(6)+10=x2-8x+12F(2):17F(6) - 490=(x.2)(x-6)(2,17)(6,49)x-2=0K-6:0x=2 x=6c)yx2-2x-3andy-3x1-3x+1=2x-ax-3POI #1POI #2F(x)=-3x+1f(x)=-3x4)0:f(x"+2x.8)(f(4)= -3(-4)+1F(2)==3(2)+1f(4)=13F(2)==50=(x+4)(x-2)(-4,13)(2,-5)X+4=6 x-2-0X--4 x=23) Determine the value of the y-intercept of a line with the given slope that is a tangent line to the givencurve.a) and a line with a slope of 1 y=1x+b62-4ac=0(4)*-4(-2)(4-6)=016-4(-8+26)=016+32-86=0-86=-486=6 b) y=-3xtb=-x2-5x-5andaline with a slope of -30=-1x7-2xt(5-b)(-2)"-46-1)(-5-b):04 - 4(5+b) : 04-20-46:0-46=166:44) The path of an underground stream is given by the function y = 4x2 + 17x - 32. Two new housesneed wells to be dug. On the area plan, these houses lie on a line defined by the equation y = - 15x +100. Determine the coordinates where the two new wells should be dug.POI 7#1POI#20 = 4x a t 32x - 132F(x)=-15xtlooF(3)=-15(3)+1000:4(x)+8x-33)F(41)==15(-11)+100F(11)=265F(3) = 550 - 1 - 88 - 330=(x+11)(x-3)(-11,265)(3,55)XHI=Ox-3-0x--11 x=3Answers1) a) do not intersect b) once c) twice d) twice2) a) (4, 3), (5,5) b) (2,17),(6,49) c) (-4,13), (2,-5)3)a)6 b) -44)(-11,265), (3,55)