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

Family of Parabolas y=(xp)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.

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

Exercise #1

Which equation represents the function:

y=x2 y=x^2

moved 2 spaces to the right

and 5 spaces upwards.

Video Solution

Answer

y=(x2)2+5 y=(x-2)^2+5

Exercise #2

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 #3

Find the corresponding algebraic representation of the drawing:

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

Video Solution

Answer

y=x24 y=x^2-4

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

Find the corresponding algebraic representation of the drawing:

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

Video Solution

Answer

y=(x5)2+4 y=(x-5)^2+4

Exercise #1

Which equation represents the function:

y=(x2)2+4 y=-(x-2)^2+4

moved 10 spaces down?

Video Solution

Answer

y=(x2)26 y=-(x-2)^2-6

Exercise #2

Find the corresponding algebraic representation of the drawing:

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

Video Solution

Answer

y=(x+10)23 y=(x+10)^2-3

Exercise #3

Which equation represents

y=(x1)2 y=(x-1)^2

moved units spaces downward?

Video Solution

Answer

y=(x1)23 y=(x-1)^2-3

Exercise #4

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 #5

Choose which equation represents the function

y=(x4)2 y=(x-4)^2

moved 2 spaces to the right

and 3 spaces upwards upwards.

Video Solution

Answer

y=(x6)2+3 y=(x-6)^2+3

Exercise #1

Which equation represents the the function

y=(x3)21 y=-(x-3)^2-1

moved 5 spaces up?

Video Solution

Answer

y=(x3)2+4 y=-(x-3)^2+4

Exercise #2

Which equation represents the function

y=x2 y=x^2

moved 4 spaces to the right

and 3 spaces upwards?

Video Solution

Answer

y=(x4)2+3 y=(x-4)^2+3

Exercise #3

Choose the equation that represents the following:

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

Video Solution

Answer

y=(x4)2+6 y=-(x-4)^2+6

Exercise #4

Which equation represents the function:

y=x2 y=-x^2

when moved 5 spaces to the right

and 4 spaces horizontally and downward?

Video Solution

Answer

y=(x5)24 y=-(x-5)^2-4

Exercise #5

Find the corresponding algebraic representation of the drawing:

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

Video Solution

Answer

y=(x5)24 y=(x-5)^2-4