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

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

$Y=X^2$

A- The basic functions Y=X²

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 $X$ .

Detailed explanation

Practice Parabola of the form y=x²

Question 1

What is the value of y for the function?

$\( y=x^2 \)$

of the point $\( x=2 \)$ ?

Question 2

Complete:

The missing value of the function point:

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

$\( f(?)=16 \)$

Question 3

What is the value of X for the function?

$\( y=x^2 \)$

of the point $\( y=4 \)$ ?

Question 4

What is the value of X for the function?

$\( y=x^2 \)$

of the point $\( y=16 \)$ ?

Question 5

What is the value of X for the function?

$\( y=x^2 \)$

of the point $\( y=36 \)$ ?

examples with solutions for parabola of the form y=x²

Exercise #1

What is the value of y for the function?

$y=x^2$

of the point $x=2$ ?

Video Solution

Answer

$y=4$

Exercise #2

Complete:

The missing value of the function point:

$f(x)=x^2$

$f(?)=16$

Video Solution

Answer

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

Exercise #3

What is the value of X for the function?

$y=x^2$

of the point $y=4$ ?

Video Solution

Answer

Answers a + b

Exercise #4

What is the value of X for the function?

$y=x^2$

of the point $y=16$ ?

Video Solution

Answer

$x=4,x=-4$

Exercise #5

What is the value of X for the function?

$y=x^2$

of the point $y=36$ ?

Video Solution

Answer

$x=\pm6$

Question 1

What is the value of y for the function?

$\( y=x^2 \)$

of the point $\( x=6 \)$ ?

Question 2

Given the function:

$\( y=x^2 \)$

Is there a point for ? $\( y=16 \)$ ?

Question 3

Given the function:

$\( y=x^2 \)$

Is there a point for ? $\( y=4 \)$ ?

Question 4

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

Question 5

Given the function:

$\( y=x^2 \)$

Is there a point for ? $\( y=-6 \)$ ?

examples with solutions for parabola of the form y=x²

Exercise #1

What is the value of y for the function?

$y=x^2$

of the point $x=6$ ?

Video Solution

Answer

$y=36$

Exercise #2

Given the function:

$y=x^2$

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

Video Solution

Answer

$(4,16)$

Exercise #3

Given the function:

$y=x^2$

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

Video Solution

Answer

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

Exercise #4

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

Video Solution

Answer

Yes

Exercise #5

Given the function:

$y=x^2$

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

Video Solution

Answer

No

Question 1

Given the function:

$\( y=x^2 \)$

Is there a point for ? $\( y=-2 \)$ ?

Question 2

Complete:

The missing value of the function point:

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

$\( f(?)=9 \)$

Question 3

Complete:

The missing value of the function point:

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

$\( f(?)=25 \)$

Question 4

What is the value of X for the function?

$\( y=x^2 \)$

of the point $\( y=25 \)$ ?

Question 5

What is the value of X for the function?

$\( y=x^2 \)$

of the point $\( y=8 \)$ ?

examples with solutions for parabola of the form y=x²

Exercise #1

Given the function:

$y=x^2$

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

Video Solution

Answer

No

Exercise #2

Complete:

The missing value of the function point:

$f(x)=x^2$

$f(?)=9$

Video Solution

Answer

Answer A+C

Exercise #3

Complete:

The missing value of the function point:

$f(x)=x^2$

$f(?)=25$

Video Solution

Answer

$f(5)$

Exercise #4

What is the value of X for the function?

$y=x^2$

of the point $y=25$ ?

Video Solution

Answer

$x=5,x=-5$

Exercise #5

What is the value of X for the function?

$y=x^2$

of the point $y=8$ ?

Video Solution

Answer

$x=\pm2\sqrt{2}$

Topics learned in later sections