Family of Parabolas y=(x-p)²+k (combination of horizontal and vertical shifts)

🏆Practice parabola of the form y=(x-p)²+k

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.

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Test yourself on parabola of the form y=(x-p)²+k!

einstein

Which equation represents the function:

\( y=x^2 \)

moved 2 spaces to the right

and 5 spaces upwards.

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Let's look at an example of combining both displacements together.

For example, in the function:
y=(x4)2+3y=(x-4)^2+3

The changes will be:
according to P=4P=4 -The parabola will shift 4 4 steps to the right.
According to K=3K=3 -The parabola will shift 3 3 steps upwards.

Let's see it in the illustration:

1 - combination of horizontal and vertical shift

We can see that the vertex of the parabola is:
(4,3)(4,3)

Zero Point or Root of the Function - Graphical and Algebraic Solution when Y=0Y=0

The zeros of a function are the intersections with the X X axis.


Algebraic Solution

when KK positive - This equation has no solution except in the case where KK equals00 and also PP equalsXX.
when KK negative- Generally, this equation will have 2 2 solutions.


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Graphical Solution

The graphical solution are the points of intersection of the parabola with the XX axis
that is, the zeros of the function.


Do you know what the answer is?

examples with solutions for 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

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