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

Question 1

Complete:

The missing value of the function point:

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

$$ f(?)=16 $$

Question 2

What is the value of y for the function?

$$ y=x^2 $$

of the point $$ x=2 $$ ?

Question 3

Given the function:

$$ y=x^2 $$

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

Question 4

Given the function:

$$ y=x^2 $$

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

Question 5

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

Examples with solutions for Parabola of the form y=x²

Exercise #1

Complete:

The missing value of the function point:

$f(x)=x^2$

$f(?)=16$

Video Solution

Answer

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

Exercise #2

What is the value of y for the function?

$y=x^2$

of the point $x=2$ ?

Video Solution

Answer

$y=4$

Exercise #3

Given the function:

$y=x^2$

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

Video Solution

Answer

Exercise #4

Given the function:

$y=x^2$

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

Video Solution

Answer

Exercise #5

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

Video Solution

Answer

Yes

Question 1

Given the function:

$$ y=x^2 $$

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

Question 2

Given the function:

$$ y=x^2 $$

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

Question 3

Complete:

The missing value of the function point:

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

$$ f(?)=9 $$

Question 4

Complete:

The missing value of the function point:

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

$$ f(?)=25 $$

Question 5

What is the value of X for the function?

$$ y=x^2 $$

of the point $$ y=4 $$ ?

Exercise #6

Given the function:

$y=x^2$

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

Video Solution

Answer

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

Exercise #7

Given the function:

$y=x^2$

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

Video Solution

Answer

$(4,16)$

Exercise #8

Complete:

The missing value of the function point:

$f(x)=x^2$

$f(?)=9$

Video Solution

Answer

Answer A+C

Exercise #9

Complete:

The missing value of the function point:

$f(x)=x^2$

$f(?)=25$

Video Solution

Answer

$f(5)$

Exercise #10

What is the value of X for the function?

$y=x^2$

of the point $y=4$ ?

Video Solution

Answer

Answers a + b

Question 1

What is the value of X for the function?

$$ y=x^2 $$

of the point $$ y=16 $$ ?

Question 2

What is the value of X for the function?

$$ y=x^2 $$

of the point $$ y=36 $$ ?

Question 3

What is the value of y for the function?

$$ y=x^2 $$

of the point $$ x=6 $$ ?

Question 4

Does the function $$ y=x^2 $$ pass through the point where y = 36 and x = 3?

Question 5

Calculate the value of $$ a $$ .

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

$$ f(4)=6+a $$

Exercise #11

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 #12

What is the value of X for the function?

$y=x^2$

of the point $y=36$ ?

Video Solution

Answer

$x=\pm6$

Exercise #13

What is the value of y for the function?

$y=x^2$

of the point $x=6$ ?

Video Solution

Answer

$y=36$

Exercise #14

Does the function $y=x^2$ pass through the point where y = 36 and x = 3?

Video Solution

Answer

Exercise #15

Calculate the value of $a$ .

$f(x)=x^2$

$f(4)=6+a$

Video Solution

Answer

$a=10$

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

The functions (y=x2,y=−x2,y=ax2)(y=x^2,y=-x^2,y=ax^2 )(y=x2,y=−x2,y=ax2)

Y=X2Y=X^2Y=X2

Practice Parabola of the form y=x²

Examples with solutions for Parabola of the form y=x²

Exercise #1

Video Solution

Answer

Exercise #2

Video Solution

Answer

Exercise #3

Video Solution

Answer

Exercise #4

Video Solution

Answer

Exercise #5

Video Solution

Answer

Exercise #6

Video Solution

Answer

Exercise #7

Video Solution

Answer

Exercise #8

Video Solution

Answer

Exercise #9

Video Solution

Answer

Exercise #10

Video Solution

Answer

Exercise #11

Video Solution

Answer

Exercise #12

Video Solution

Answer

Exercise #13

Video Solution

Answer

Exercise #14

Video Solution

Answer

Exercise #15

Video Solution

Answer

Topics learned in later sections

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

$Y=X^2$