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

2024
Views:

280

Pages:

4
Author:

J. Anderson

1.6 Determine a Quadratic Equation Given its Roots - WorksheetMCR3UlensenSOLUTIONS1) Find the equation of a quadratic function that has the given x-intercepts and contains the given point.Express each function in factored form.5 $xyr Sa) -3 and 5, point (4,-3)b) -4 and 7, point (-3,-y=a(x-r)(x-s)y=a(x-s)(x-s)-3:a(4+3)(4-5)-12=a(-3+4)(-3-7)-12 : a(1)(-10)3-7a12:10aa - 3/79-12/10a=6/5y=3(a)3)x-5)2) Express each function from #1 in standard form.a)b)y,362.2x-15)4-5(x3-38-28)3) Find the equation of a quadratic function that has the given x-intercepts and contains the given point.Express each function in standard form.a) 1 point (4,-6) xyb)-2 + v7, point (1,2)y:a(x-r)(x.s)y=alx-xxx-s)y=a(xr2-55)(1422+py=3(x2-2x-10)y=a(x2-2x-10)y=1(xx+4x-3)sub point*subpoint-6=a[(4)-244)-10]2=a((1)7+4(1)-3]y=xx+4x-31-6/21-2)2 a(2)a=3a=l Sx y4) Find the equation of the quadratic function that has zeros at 3 and 1 and contains the point (1,-2).Express the function in vertex form.complete squae:y=a(x-r)(x-s)y=-2=a(1-3)(1+1)y=1(x2-2x-3)-2=a(-4)a=1/2y=j:5) Determine the equation in standard form for each quadratic function shown.a)b)YAy603(-2,0)(13,0)4020024S2T-4-2024(4,-3)x4-20y:a(x-r)(x-s)f(x) = a(x-r)(x.s)28=a(2+5)(2-3)-3=a(6)28=a(7)(-1)28 - 7aa==1/2a=-4y=-4(x+5)(x-3)Y:-4(x3+2x-15)y - 4x - 8x 460 6) An arch of a highway overpass is in the shape of a parabola. The arch spans a distance of 12 metersfrom one side of the road to the other. The height of the arch is 8 meters at a horizontal distance of 2meters from each side of the arch.a) Sketch the quadratic function if the vertex of the parabola is on the y-axis and the road is along the X-axis.(4,8)b) Use this information to determine the function that models the arch. (-6,0)(6,0)y=a(x-r)(-s)8:a(4+6)(4-6)8-9(10)(-2)9=-820a==2/5) Find the maximum height of the arch to the nearest tenth of a meter.Answers1) a)f(x)="(x+3)(x-5)2)3)a)f(x)=3x2-6x-30 b)f(x)=x2+4x-3 =b)f(x)=-4x2-8x60