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

### Family of Parabolas$y=(x-p)²+k$

Combination of Horizontal and Vertical Shift
$K$ determines the amount of steps and the vertical direction in which the function will shift - upwards or downwards.
$P$ determines the amount of steps and the horizontal direction in which the function will shift - to the right or to the left.

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

### Exercise #1

Which equation represents the function:

$y=x^2$

moved 2 spaces to the right

and 5 spaces upwards.

### Video Solution

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

### Exercise #2

Find the corresponding algebraic representation of the drawing:

### Video Solution

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

### Exercise #3

Find the corresponding algebraic representation of the drawing:

### Video Solution

$y=x^2-4$

### Exercise #4

Choose the equation that represents the function

$y=-x^2$

moved 3 spaces to the left

and 4 spaces up.

### Video Solution

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

### Exercise #5

Find the corresponding algebraic representation of the drawing:

### Video Solution

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

### Exercise #1

Which equation represents the function:

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

moved 10 spaces down?

### Video Solution

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

### Exercise #2

Find the corresponding algebraic representation of the drawing:

### Video Solution

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

### Exercise #3

Which equation represents

$y=(x-1)^2$

moved units spaces downward?

### Video Solution

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

### Exercise #4

Choose the equation that corresponds to the function

$y=x^2$

moved 10 spaces up.

### Video Solution

$y=x^2+10$

### Exercise #5

Choose which equation represents the function

$y=(x-4)^2$

moved 2 spaces to the right

and 3 spaces upwards upwards.

### Video Solution

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

### Exercise #1

Which equation represents the the function

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

moved 5 spaces up?

### Video Solution

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

### Exercise #2

Which equation represents the function

$y=x^2$

moved 4 spaces to the right

and 3 spaces upwards?

### Video Solution

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

### Exercise #3

Choose the equation that represents the following:

### Video Solution

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

### Exercise #4

Which equation represents the function:

$y=-x^2$

when moved 5 spaces to the right

and 4 spaces horizontally and downward?

### Video Solution

$y=-(x-5)^2-4$
$y=(x-5)^2-4$