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
Questions & Answers
Biology is a branch of Natural science which deals/About living Organism.
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things