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=X2Y=X^2
image - The basic functions   Y=X²

Properties of the function:

The most basic quadratic function b=0b=0,c=0c=0
Minimum, happy face function, its vertex is (0,0)(0,0)
The axis of symmetry of this function is X=0X=0.
The function's interval of increase: X>0X>0
The function's interval of decrease: X<0X<0
Set of positivity: Every XX except 00.
Set of negativity: None. The entire parabola is above the axisXX.

Practice Parabola of the form y=x²

Exercise #1

What is the value of y for the function?

y=x2 y=x^2

of the point x=2 x=2 ?

Video Solution

Answer

y=4 y=4

Exercise #2

Complete:

The missing value of the function point:

f(x)=x2 f(x)=x^2

f(?)=16 f(?)=16

Video Solution

Answer

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

Exercise #3

What is the value of X for the function?

y=x2 y=x^2

of the point y=36 y=36 ?

Video Solution

Answer

x=±6 x=\pm6

Exercise #4

What is the value of y for the function?

y=x2 y=x^2

of the point x=6 x=6 ?

Video Solution

Answer

y=36 y=36

Exercise #5

Given the function:

y=x2 y=x^2

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

Video Solution

Answer

No

Exercise #1

Given the function:

y=x2 y=x^2

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

Video Solution

Answer

No

Exercise #2

Does the function y=x2 y=x^2 pass through the point where y = 36 and x = 6?

Video Solution

Answer

Yes

Exercise #3

Given the function:

y=x2 y=x^2

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

Video Solution

Answer

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

Exercise #4

Given the function:

y=x2 y=x^2

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

Video Solution

Answer

(4,16) (4,16)

Exercise #5

Complete:

The missing value of the function point:

f(x)=x2 f(x)=x^2

f(?)=9 f(?)=9

Video Solution

Answer

Answer A+C

Exercise #1

Complete:

The missing value of the function point:

f(x)=x2 f(x)=x^2

f(?)=25 f(?)=25

Video Solution

Answer

f(5) f(5)

Exercise #2

What is the value of X for the function?

y=x2 y=x^2

of the point y=4 y=4 ?

Video Solution

Answer

Answers a + b

Exercise #3

What is the value of X for the function?

y=x2 y=x^2

of the point y=16 y=16 ?

Video Solution

Answer

x=4,x=4 x=4,x=-4

Exercise #4

What is the value of y for the function?

y=x2 y=x^2

of the point x=10 x=10 ?

Video Solution

Answer

y=100 y=100

Exercise #5

What is the value of y for the function?

y=x2 y=x^2

of the point x=12 x=12 ?

Video Solution

Answer

y=144 y=144

Topics learned in later sections

  1. Families of Parabolas
  2. Family of Parabolas y=x²+c: Vertical Shift
  3. Family of Parabolas y=(x-p)²
  4. Family of Parabolas y=(x-p)²+k (combination of horizontal and vertical shifts)