Family of Parabolas y=x²+c: Vertical Shift

Parabola of the Form y=x²+c - Examples, Exercises and Solutions

Family of Parabolas $y=x²+c$ : Vertical Shift

The basic quadratic function $y=x^2$ with the addition of $C$ yields the function $y=x^2+c$
The meaning of $C$ is the vertical shift of the function upwards or downwards.
If $C$ is positive: the function will rise by the number of steps shown in $C$ .
If $C$ is negative: the function will descend by the number of steps shown in $C$ .

Detailed explanation

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Test yourself on parabola of the form y=x²+c!

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Find the ascending area of the function

$\( f(x)=2x^2 \)$

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Let's look at an example

$y=x^2+3$
The function will rise three steps.

1 - Vertical shift

Additionally, we can see that $C$ marks the intersection point on the $Y$ axis.

Examples and exercises with solutions from the family of parabolas y=x²+c

Exercise #1

Find the ascending area of the function

$f(x)=2x^2$

Video Solution

Answer

$0 < x$

Exercise #2

Find the descending area of the function

$f(x)=\frac{1}{2}x^2$

Video Solution

Answer

$x < 0$

Exercise #3

One function

$y=-2x^2-3$

to the corresponding graph:

Video Solution

Answer

4

Exercise #4

One function

$y=6x^2$

to the corresponding graph:

Video Solution

Answer

2

Exercise #5

One function

$y=-6x^2$

to the corresponding graph:

Video Solution

Answer

4

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Test your knowledge

Question 1

Find the descending area of the function

$f(x)=\frac{1}{2}x^2$

Question 2

One function

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

to the corresponding graph:

Question 3

One function

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

to the corresponding graph:

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