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Nonlinear Equations and Functions Questions - All Grades

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Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.3

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It can be shown that the value b from the previous question relates to the vertices of the minor-axis. Specifically, the vertices are (0,-b) and (0,b). Looking at the positive vertex, it forms an isosceles triangle with the two foci. What is the length of the two congruent sides? How is this related to the previous question?
  1. They each have a length of 2c. Using the distance formula and looking at the difference of distances between the lengths just found and the other vertices of the major axes, one finds that b=a2-c2.
  2. They each have a length of c. Then, the right triangle formed between the vertices and the origin, and applying the Pythagorean theorem, results in a2+b2=c2.
  3. They each have a length of a. Looking at the right triangle formed by the origin, F1, and the vertex (0,b), and applying the Pythagorean theorem results in a2=b2+c2.
  4. They each have a length of a2. Therefore, the sum of their lengths, a, can be used as a value equal to the sum of the lengths of b and c.
Grade 11 Nonlinear Equations and Functions

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Using the distances between the two foci and the vertex (-a,0), what does d1+d2 equal?
  1. d1+d2=2a-c
  2. d1+d2=2a-c
  3. d1+d2=2a
  4. d1+d2=c
Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.1

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Grade 11 Nonlinear Equations and Functions
Factor and solve. x3-64=0
  1. -4,2±2i3
  2. 4,-2±2i3
  3. 2,-4±4i3
  4. -4,4±4i3
Grade 9 Nonlinear Equations and Functions CCSS: HSA-CED.A.4
Solve for x.

3xy+4=xy-8
  1. x=-6y
  2. x=-2y
  3. x=3y
  4. x=2y
  5. x=6y
Grade 11 Nonlinear Equations and Functions
Grade 11 Nonlinear Equations and Functions
Given the equation of a hyperbola (y-5)216-(x+3)24=1, identify the foci.
  1. (-3±25,0)
  2. (0,5±25)
  3. (5±5,-3)
  4. (-3,5±25)
Grade 11 Nonlinear Equations and Functions
Grade 11 Nonlinear Equations and Functions
Which equation represents the ellipse with foci on the x-axis, major axis 9 units long, minor axis 4 units long, and center at the origin?
  1. x24+y29=1
  2. x220.25+y24=1
  3. x29+y24=1
  4. x24+y220.25=1
Grade 11 Nonlinear Equations and Functions
Grade 11 Nonlinear Equations and Functions
What are the solutions of 2x3+4x2-20x=10x+60?
  1. 15,-15
  2. 2,15,-15
  3. -2,15,-15
  4. 2,15
Grade 11 Nonlinear Equations and Functions
Given the equation of ellipse x225+y216=1, identify the foci.
  1. (±3,0)
  2. (0,±3)
  3. (±41,0)
  4. (0,±41)
Grade 11 Nonlinear Equations and Functions
Grade 10 Nonlinear Equations and Functions CCSS: HSA-REI.A.2
Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.2
What is the equation of a parabola with the focus at (4,-5) and directrix x=0?
  1. (y-5)2=8x
  2. (y+5)2=8(x-4)
  3. (y+5)2=8x-16
  4. (y-5)2+8=4x
Grade 11 Nonlinear Equations and Functions
Identify the directrix of y=-2x2.
  1. y=-2
  2. y=12
  3. y=18
  4. y=-18
Grade 11 Nonlinear Equations and Functions
Grade 11 Nonlinear Equations and Functions
Grade 10 Nonlinear Equations and Functions
How many solutions does y in 34y+33y=74y have?
  1. 1 solution
  2. 2 solutions
  3. no solutions
  4. Infinitely many
Grade 11 Nonlinear Equations and Functions
Identify the focus of y=4x2.
  1. (0,14)
  2. (116,0)
  3. (0,116)
  4. (14,0)
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