# The functions y=x²

🏆Practice parabola of the form y=x²

### The functions$(y=x^2,y=-x^2,y=ax^2 )$

##### $Y=X^2$

Properties of the function:

The most basic quadratic function $b=0$,$c=0$
Minimum, happy face function, its vertex is $(0,0)$
The axis of symmetry of this function is $X=0$.
The function's interval of increase: $X>0$
The function's interval of decrease: $X<0$
Set of positivity: Every $X$ except $0$.
Set of negativity: None. The entire parabola is above the axis$X$.

## Test yourself on parabola of the form y=x²!

Complete:

The missing value of the function point:

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

$$f(?)=16$$

### Properties of the Function

The most basic quadratic function $a=-1$,$b=0$,$c=0$
Maximum, sad face function, its vertex is $(0,0)$
The axis of symmetry of this function is $X=0$.
The interval of increase of the function: $X<0$
The interval of decrease of the function: $X>0$
Set of positivity: None. The entire parabola is below the axis$X$.
Set of negativity: All $X$ except for $X=0$

$y=ax^2$

Properties of the function:
$any number = a$,$b=0$,$c=0$

Its vertex is $(0,0)$
The axis of symmetry of this function is $X=0$.

As $a$  increases, the parabola will have a smaller opening - closer to its axis of symmetry.
As $a$  decreases, the parabola will have a larger opening - further from its axis of symmetry.

## Examples and exercises with solutions for the functions y=x²

### Exercise #1

Complete:

The missing value of the function point:

$f(x)=x^2$

$f(?)=16$

### Video Solution

$f(4)$$f(-4)$

### Exercise #2

What is the value of y for the function?

$y=x^2$

of the point $x=2$?

### Video Solution

$y=4$

### Exercise #3

Given the function:

$y=x^2$

Is there a point for ? $y=-2$?

No

### Exercise #4

Given the function:

$y=x^2$

Is there a point for ? $y=-6$?

No

### Exercise #5

Does the function $y=x^2$ pass through the point where y = 36 and x = 6?