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Nonlinear Equations and Functions Questions - All Grades

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

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Grade 11 Nonlinear Equations and Functions

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Squaring both sides, expanding, and combing like terms, dividing by any common constants, and putting all terms without a square root on the left side of the equation results in which of the following equations?
  1. 2cx-a=0
  2. cx±a2=-2(x-c)2+y2
  3. cx-a2=0
  4. cx-a2=±a(x-c)2+y2
Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.3

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Let (x,y) be a point on the hyperbola. What is the distance, d1, between F1 and the point (x,y)?
  1. d1=(x+c)2+y2
  2. d1=(x-c)2+y2
  3. d1=(x2+y2)
  4. d1=(x-c)2+(y-c)2
Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.3

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Substitute the equations for d1,d2 found in the second and third questions into the equation in the previous question. After some rearranging, the result is the following equation:

(x+c)2+y2=±2a+(x-c)2+y2

Why is there a plus-minus sign on the 2a term?
  1. In order to remove the absolute value sign, one has to consider the case where d1>d2 and d1<d2.
  2. To remove the square root from this term, one has to look at the positive and negative case.
  3. Since it's not certain which side of the equation this term should be on, it could be either positive or negative.
  4. This is a hyperbola and the curves can be on either the positive or negative x-axis.
Grade 11 Nonlinear Equations and Functions
Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.1

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Grade 11 Nonlinear Equations and Functions
Grade 11 Nonlinear Equations and Functions
Solve x3=216.
  1. x=9
  2. x=6
  3. x=81
  4. x=27
Grade 11 Nonlinear Equations and Functions CCSS: HSA-REI.A.2
Solve. Check for extraneous solutions.

xx-1=x+3-2x+2
  1. x=-1orx=-2
  2. x=-1
  3. x=1
  4. x=1orx=-1
Grade 10 Nonlinear Equations and Functions CCSS: HSA-REI.A.2
If x-1x=4, then x=
  1. 3
  2. -3
  3. -16
  4. -13
Grade 11 Nonlinear Equations and Functions
The equation x2+y2+2x+1=0 represents
  1. a point.
  2. a circle.
  3. a parabola.
  4. an ellipse.
Grade 10 Nonlinear Equations and Functions
Grade 11 Nonlinear Equations and Functions
Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.2
What is the equation of a parabola with the focus at (1,3) and a directrix of x=-5?
  1. (x-3)2=12(y+2)
  2. (y-3)2=12(x-1)
  3. (y+3)2=3(x-2)
  4. (y-3)2=12(x+2)
Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.3

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What does |d1-d2| equal?
  1. |d1-d2|=a
  2. |d1-d2|=c
  3. |d1-d2|=|a-c|
  4. |d1-d2|=2a
Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.3

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

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What is the distance, d2, between the F2 and the point (x,y)?
  1. d2=(x-c)2+(y-c)2
  2. d2=x2+y2
  3. d2=(x+c)2+y2
  4. d2=(x-c)2+y2
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