The Family of Parabolas

The function \(y=x^2\)

The family of parabolas \(y=x²+c\)

The family of parabolas \(y=(x-p)²\)

The family of parabolas \(y=(x-p)²+k\)

Practice Forms of Parabolas

Exercise #1

What is the positive domain of the function below?

y=(x2)2 y=(x-2)^2

Video Solution

Step-by-Step Solution

In the first step, we place 0 in place of Y:

0 = (x-2)²

 

We perform a square root:

0=x-2

x=2

And thus we reveal the point

(2, 0)

This is the vertex of the parabola.

 

Then we decompose the equation into standard form:

 

y=(x-2)²

y=x²-4x+2

Since the coefficient of x² is positive, we learn that the parabola is a minimum parabola (smiling).

If we plot the parabola, it seems that it is actually positive except for its vertex.

Therefore the domain of positivity is all X, except X≠2.

 

Answer

all x, x2 x\ne2

Exercise #2

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 #3

Find the ascending area of the function

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

Video Solution

Answer

0 < x

Exercise #4

One function

y=6x2 y=-6x^2

to the corresponding graph:

1234

Video Solution

Answer

4

Exercise #5

One function

y=2x23 y=-2x^2-3

to the corresponding graph:

333333-3-3-3333-3-3-3-3-3-31234

Video Solution

Answer

4

Exercise #1

One function

y=6x2 y=6x^2

to the corresponding graph:

1234

Video Solution

Answer

2

Exercise #2

Which chart represents the function y=x29 y=x^2-9 ?

222333999-9-9-9-1-1-1444-101234

Video Solution

Answer

4

Exercise #3

Find the descending area of the function

f(x)=12x2 f(x)=\frac{1}{2}x^2

Video Solution

Answer

x < 0

Exercise #4

Find the intersection of the function

y=(x+4)2 y=(x+4)^2

With the Y

Video Solution

Answer

(0,16) (0,16)

Exercise #5

Find the intersection of the function

y=(x2)2 y=(x-2)^2

With the X

Video Solution

Answer

(2,0) (2,0)

Exercise #1

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 #2

To work out the points of intersection with the X axis, you must substitute x=0 x=0 .

Video Solution

Answer

False

Exercise #3

To find the y axis intercept, you substitute x=0 x=0 into the equation and solve for y.

Video Solution

Answer

True

Exercise #4

To which chart does the function y=x2 y=x^2 correspond?

1234

Video Solution

Answer

2

Exercise #5

One function

y=x2 y=-x^2

for the corresponding chart

-1-1-11234

Video Solution

Answer

2