# 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 $C$

### Suggested Topics to Practice in Advance

1. The functions y=x²

## Examples with solutions for Parabola of the Form y=x²+c

### Exercise #1

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

4

### Exercise #2

One function

$y=-6x^2$

to the corresponding graph:

4

### Exercise #3

One function

$y=-2x^2-3$

to the corresponding graph:

4

### Exercise #4

One function

$y=6x^2$

to the corresponding graph:

2

### Exercise #5

Find the ascending area of the function

$f(x)=2x^2$

0 < x

### Exercise #6

Find the descending area of the function

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

x < 0

### Exercise #7

One function

$y=x^2+9$

to the corresponding graph:

3

### Exercise #8

One function

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

to the corresponding graph:

1

### Exercise #9

One function

$y=-\frac{1}{2}x^2+4$

to the corresponding graph:

1

### Exercise #10

Find the corresponding algebraic representation for the function

### Video Solution

$y=x^2-6$

### Exercise #11

Find the corresponding algebraic representation for the function

### Video Solution

$y=-x^2+1$

### Exercise #12

Match the function $y=2x^2+3$

to the corresponding graph.

3

### Exercise #13

Choose the increasing and decreasing domains of the following function:

$f(x)=-2x^2+10$

0 < x decreasing

x < 0 increasing

### Exercise #14

Find the positive area of the function

$f(x)=x^2$

### Video Solution

$x≠0$

### Exercise #15

Find the negative area of the function

$f(x)=-x^2$