Parabola of the Form y=(x-p)²+k - Examples, Exercises and Solutions

Question Types:
Parabola of the Form y=(x-p)²+k: Identify the positive and negative domainParabola of the Form y=(x-p)²+k: Finding a stationary pointParabola of the Form y=(x-p)²+k: Finding Increasing or Decreasing DomainsParabola of the Form y=(x-p)²+k: Determine the algebraic representation of the following descriptions

Family of Parabolas y=(x−p)2+k y=(x-p)²+k

Combination of Horizontal and Vertical Shift
In this quadratic function 
KK determines the amount of steps and the vertical direction in which the function will shift - upwards or downwards.
PP determines the amount of steps and the horizontal direction in which the function will shift - to the right or to the left.

Detailed explanation

Suggested Topics to Practice in Advance

  1. The functions y=x²
  2. Families of Parabolas
  3. Family of Parabolas y=x²+c: Vertical Shift
  4. Family of Parabolas y=(x-p)²

Practice Parabola of the Form y=(x-p)²+k

Question 1

Find the corresponding algebraic representation of the drawing:

(0,-4)(0,-4)(0,-4)

Question 2

Find the corresponding algebraic representation of the drawing:

(5,4)(5,4)(5,4)

Question 3

Find the corresponding algebraic representation of the drawing:

(-2,7)(-2,7)(-2,7)

Question 4

Choose the equation that represents the function

\( y=-x^2 \)

moved 3 spaces to the left

and 4 spaces up.

Question 5

Which equation represents the function:

\( y=x^2 \)

moved 2 spaces to the right

and 5 spaces upwards.

Examples with solutions for Parabola of the Form y=(x-p)²+k

Exercise #1

Find the corresponding algebraic representation of the drawing:

(0,-4)(0,-4)(0,-4)

Video Solution

Answer

y=x2−4 y=x^2-4

Exercise #2

Find the corresponding algebraic representation of the drawing:

(5,4)(5,4)(5,4)

Video Solution

Answer

y=(x−5)2+4 y=(x-5)^2+4

Exercise #3

Find the corresponding algebraic representation of the drawing:

(-2,7)(-2,7)(-2,7)

Video Solution

Answer

y=(x+2)2+7 y=(x+2)^2+7

Exercise #4

Choose the equation that represents the function

y=−x2 y=-x^2

moved 3 spaces to the left

and 4 spaces up.

Video Solution

Answer

y=−(x+3)2+4 y=-(x+3)^2+4

Exercise #5

Which equation represents the function:

y=x2 y=x^2

moved 2 spaces to the right

and 5 spaces upwards.

Video Solution

Answer

y=(x−2)2+5 y=(x-2)^2+5

Question 1

Choose the equation that corresponds to the function

\( y=(x-2)^2 \)

moved 3 spaces up.

Question 2

Which equation represents

\( y=(x-1)^2 \)

moved units spaces downward?

Question 3

Choose the equation that corresponds to the function

\( y=x^2 \)

moved 10 spaces up.

Question 4

Which equation represents the the function

\( y=-(x-3)^2-1 \)

moved 5 spaces up?

Question 5

Which equation represents the function:

\( y=-(x-2)^2+4 \)

moved 10 spaces down?

Exercise #6

Choose the equation that corresponds to the function

y=(x−2)2 y=(x-2)^2

moved 3 spaces up.

Video Solution

Answer

y=(x−2)2+3 y=(x-2)^2+3

Exercise #7

Which equation represents

y=(x−1)2 y=(x-1)^2

moved units spaces downward?

Video Solution

Answer

y=(x−1)2−3 y=(x-1)^2-3

Exercise #8

Choose the equation that corresponds to the function

y=x2 y=x^2

moved 10 spaces up.

Video Solution

Answer

y=x2+10 y=x^2+10

Exercise #9

Which equation represents the the function

y=−(x−3)2−1 y=-(x-3)^2-1

moved 5 spaces up?

Video Solution

Answer

y=−(x−3)2+4 y=-(x-3)^2+4

Exercise #10

Which equation represents the function:

y=−(x−2)2+4 y=-(x-2)^2+4

moved 10 spaces down?

Video Solution

Answer

y=−(x−2)2−6 y=-(x-2)^2-6

Question 1

Choose the equation that corresponds to the the function

\( y=-(x-6)^2 \)

moved 4 spaces up.

Question 2

Choose the equation that represents the following:

(4,6)(4,6)(4,6)

Question 3

Find the corresponding algebraic representation of the drawing:

(8,-2)(8,-2)(8,-2)

Question 4

Find the corresponding algebraic representation of the drawing:

(-10,-3)(-10,-3)(-10,-3)

Question 5

Find the corresponding algebraic representation of the drawing:

(5,-4)(5,-4)(5,-4)

Exercise #11

Choose the equation that corresponds to the the function

y=−(x−6)2 y=-(x-6)^2

moved 4 spaces up.

Video Solution

Answer

y=−(x−6)2+4 y=-(x-6)^2+4

Exercise #12

Choose the equation that represents the following:

(4,6)(4,6)(4,6)

Video Solution

Answer

y=−(x−4)2+6 y=-(x-4)^2+6

Exercise #13

Find the corresponding algebraic representation of the drawing:

(8,-2)(8,-2)(8,-2)

Video Solution

Answer

y=−(x−8)2−2 y=-(x-8)^2-2

Exercise #14

Find the corresponding algebraic representation of the drawing:

(-10,-3)(-10,-3)(-10,-3)

Video Solution

Answer

y=(x+10)2−3 y=(x+10)^2-3

Exercise #15

Find the corresponding algebraic representation of the drawing:

(5,-4)(5,-4)(5,-4)

Video Solution

Answer

y=(x−5)2−4 y=(x-5)^2-4