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

Practice Parabola of the form y=x²+c

Question 1

Find the ascending area of the function

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

Question 2

Find the descending area of the function

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

Question 3

Which chart represents the function $$ y=x^2-9 $$ ?

Question 4

One function

$$ y=6x^2 $$

to the corresponding graph:

Question 5

One function

$$ y=-6x^2 $$

to the corresponding graph:

examples with solutions for parabola of the form 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

Which chart represents the function $y=x^2-9$ ?

Video Solution

Answer

Exercise #4

One function

$y=6x^2$

to the corresponding graph:

Video Solution

Answer

Exercise #5

One function

$y=-6x^2$

to the corresponding graph:

Video Solution

Answer

Question 1

One function

$$ y=-2x^2-3 $$

to the corresponding graph:

Question 2

Find the corresponding algebraic representation for the function

Question 3

Find the corresponding algebraic representation for the function

Question 4

One function

$$ y=x^2+9 $$

to the corresponding graph:

Question 5

One function

$y=\frac{x^2}{4}+2$

to the corresponding graph: