Writing the equation of a quadratic function from the graph
Write an equation for the quadratic function
in
[link] as a transformation of
and then expand the formula, and simplify terms to write the equation in general form.
We can see the graph of
g is the graph of
shifted to the left 2 and down 3, giving a formula in the form
Substituting the coordinates of a point on the curve, such as
we can solve for the stretch factor.
In standard form, the algebraic model for this graph is
To write this in general polynomial form, we can expand the formula and simplify terms.
Notice that the horizontal and vertical shifts of the basic graph of the quadratic function determine the location of the vertex of the parabola; the vertex is unaffected by stretches and compressions.
A coordinate grid has been superimposed over the quadratic path of a basketball in
[link] . Find an equation for the path of the ball. Does the shooter make the basket?
The path passes through the origin and has vertex at
so
To make the shot,
would need to be about 4 but
he doesn’t make it.
Finding the domain and range of a quadratic function
Any number can be the input value of a quadratic function. Therefore, the domain of any quadratic function is all real numbers. Because parabolas have a maximum or a minimum point, the range is restricted. Since the vertex of a parabola will be either a maximum or a minimum, the range will consist of all
y -values greater than or equal to the
y -coordinate at the turning point or less than or equal to the
y -coordinate at the turning point, depending on whether the parabola opens up or down.
Domain and range of a quadratic function
The domain of any
quadratic function is all real numbers.
The range of a quadratic function written in general form
with a positive
value is
or
the range of a quadratic function written in general form with a negative
value is
or
The range of a quadratic function written in standard form
with a positive
value is
the range of a quadratic function written in standard form with a negative
value is
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature