# Forms of Parabolas - Examples, Exercises and Solutions

## Practice Forms of Parabolas

### Exercise #1

What is the positive domain of the function below?

$y=(x-2)^2$

### 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.

all x, $x\ne2$

### Exercise #2

What is the value of y for the function?

$y=x^2$

of the point $x=2$?

### Video Solution

$y=4$

### Exercise #3

Find the ascending area of the function

$f(x)=2x^2$

0 < x

### Exercise #4

One function

$y=-6x^2$

to the corresponding graph:

4

### Exercise #5

One function

$y=-2x^2-3$

to the corresponding graph:

4

### Exercise #1

One function

$y=6x^2$

to the corresponding graph:

2

### Exercise #2

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

4

### Exercise #3

Find the descending area of the function

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

x < 0

### Exercise #4

Find the intersection of the function

$y=(x+4)^2$

With the Y

### Video Solution

$(0,16)$

### Exercise #5

Find the intersection of the function

$y=(x-2)^2$

With the X

### Video Solution

$(2,0)$

### Exercise #1

Complete:

The missing value of the function point:

$f(x)=x^2$

$f(?)=16$

### Video Solution

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

### Exercise #2

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

False

### Exercise #3

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

True

### Exercise #4

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

2

### Exercise #5

One function

$y=-x^2$

for the corresponding chart