the most basic quadratic function:
![Parabola y=X²](/_ipx/f_png,s_500x500/https://cdn.tutorela.com/images/1_Families_of_Parabolas.width-500.png)
the most basic quadratic function:
The family of parabolas
The basic quadratic function – with the addition of
In this family, we are given a quadratic function that clearly shows us how the function moves horizontally – how many steps it needs to move right or left.
represents the number of steps the function will move horizontally – right or left.
If is positive – (there is a minus in the equation) – the function will move steps to the right.
If is negative – (and as a result, there is a plus in the equation because minus times minus equals plus) – the function will move steps to the left.
In this quadratic function, we can see a combination of horizontal and vertical shifts:
: Determines the number of steps and the direction the function will move vertically – up or down.
positive – shift up, negative – shift down.
: Determines the number of steps and the direction the function will move horizontally – right or left.
What is the positive domain of the function below?
\( y=(x-2)^2 \)
Find the intersection of the function
\( y=(x+4)^2 \)
With the Y
Find the intersection of the function
\( y=(x-2)^2 \)
With the X
What is the value of y for the function?
\( y=x^2 \)
of the point \( x=2 \)?
Complete:
The missing value of the function point:
\( f(x)=x^2 \)
\( f(?)=16 \)
What is the positive domain of the function below?
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,
Find the intersection of the function
With the Y
Find the intersection of the function
With the X
What is the value of y for the function?
of the point ?
Complete:
The missing value of the function point:
Find the ascending area of the function
\( f(x)=2x^2 \)
Find the descending area of the function
\( f(x)=\frac{1}{2}x^2 \)
Which chart represents the function \( y=x^2-9 \)?
One function
\( y=6x^2 \)
to the corresponding graph:
One function
\( y=-6x^2 \)
to the corresponding graph:
Find the ascending area of the function
0 < x
Find the descending area of the function
x < 0
Which chart represents the function ?
4
One function
to the corresponding graph:
2
One function
to the corresponding graph:
4
One function
\( y=-2x^2-3 \)
to the corresponding graph:
Find the intersection of the function
\( y=(x-2)^2 \)
With the Y
Find the intersection of the function
\( y=(x-6)^2 \)
With the Y
Find the positive area of the function
\( y=(x+6)^2 \)
Find the positive area of the function
\( y=(x+5)^2 \)
One function
to the corresponding graph:
4
Find the intersection of the function
With the Y
Find the intersection of the function
With the Y
Find the positive area of the function
Find the positive area of the function
For each X