# Parabola of the form y=x² - Examples, Exercises and Solutions

### 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$X$.

## Practice Parabola of the form y=x²

### Exercise #1

What is the value of y for the function?

$y=x^2$

of the point $x=2$?

### Answer

$y=4$

### Exercise #2

Complete:

The missing value of the function point:

$f(x)=x^2$

$f(?)=16$

### Answer

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

### Exercise #3

What is the value of X for the function?

$y=x^2$

of the point $y=36$?

### Answer

$x=\pm6$

### Exercise #4

What is the value of y for the function?

$y=x^2$

of the point $x=6$?

### Answer

$y=36$

### Exercise #5

Given the function:

$y=x^2$

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

No

### Exercise #1

Given the function:

$y=x^2$

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

No

### Exercise #2

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

Yes

### Exercise #3

Given the function:

$y=x^2$

Is there a point for ? $y=4$?

### Answer

$(2,4)$$(-2,4)$

### Exercise #4

Given the function:

$y=x^2$

Is there a point for ? $y=16$?

### Answer

$(4,16)$

### Exercise #5

Complete:

The missing value of the function point:

$f(x)=x^2$

$f(?)=9$

Answer A+C

### Exercise #1

Complete:

The missing value of the function point:

$f(x)=x^2$

$f(?)=25$

### Answer

$f(5)$

### Exercise #2

What is the value of X for the function?

$y=x^2$

of the point $y=4$?

Answers a + b

### Exercise #3

What is the value of X for the function?

$y=x^2$

of the point $y=16$?

### Answer

$x=4,x=-4$

### Exercise #4

What is the value of y for the function?

$y=x^2$

of the point $x=10$?

### Answer

$y=100$

### Exercise #5

What is the value of y for the function?

$y=x^2$

of the point $x=12$?

### Answer

$y=144$