Forms of Parabolas - Examples, Exercises and Solutions

What is the positive domain of the function below?

$y=(x-2)^2$

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.

all x, $x\ne2$

Find the intersection of the function

$y=(x+4)^2$

With the Y

$(0,16)$

Find the intersection of the function

$y=(x-2)^2$

With the X

$(2,0)$

What is the value of y for the function?

$y=x^2$

of the point $x=2$?

$y=4$

Complete:

The missing value of the function point:

$f(x)=x^2$

$f(?)=16$

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

Find the ascending area of the function

$f(x)=2x^2$

0 < x

Find the descending area of the function

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

x < 0

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

4

One function

$y=6x^2$

to the corresponding graph:

2

One function

$y=-6x^2$

to the corresponding graph:

4

One function

$y=-2x^2-3$

to the corresponding graph:

4

Find the intersection of the function

$y=(x-2)^2$

With the Y

$(0,4)$

Find the intersection of the function

$y=(x-6)^2$

With the Y

$(0,36)$

Find the positive area of the function

$y=(x+6)^2$

$x\ne-6$

Find the positive area of the function
$y=(x+5)^2$

For each X $x\ne5$