Comparing And Contrasting Linear Functions and Quadratic Functions

Comparing And Contrasting Linear Functions & Quadratic Functions
A quadratic function is similar to a
linear function by...
Both graphs on a line
Both used in our daily activities
Linear: Walking at a normal pace.... since you
are walking at a normal pace your ability to
walk more will increase (over time)
Quadratic: When you are doing your
homework for a long time... if you are doing
your homework for a long time, you will most
likely get bored and do something else
The equation of a linear function is y=mx=b
Linear Functions:
A function that is a straight line on a
graph
The m in the equation is the slope(rise/run).
The b in the equation is the y intercept.
Linear functions (on a graph) is a straight line.
It can be positive or negative
You can have positive slopes(increasing) as
shown above.
Or even negative slopes(decreasing) in linear
functions
An example of not a linear function may be
y^2=0. This not an example of a linear
function because it is not is slopeintercept
form as above. ^^^^
An example of a linear function are these stairs.
As you go up the stairs the slope (in a linear
function) increases
Another one is this seesaw because it is at
an angle
A quadratic function is any function that can
be written in the form y=ax^2+bx+c
Quadratic Functions
In quadratic functions, the graph is a parabola
which is U shaped^^^
Parabola 's have an axis of symmetry (divides
the parabola in two halves. The formula to
find the A.O.S is b/2a.
In the example: y=3x^26x+1, the 3 would be
the a.  The 6 is the b and the 1 is the c.
Parabola 's  in quadratic functions have a vertex.
Depending on the parabola, it is the highest or
lowest point. To find the vertex, you first have
to find the A.O.S (which is the x value). Then
substitute that to find the y and that 's how you
get the vertex.
This is a banana which is a quadratic function
Another example of a parabola is this baseball being thrown
Parabola 's can have a minimum
(smiley face) or a maximum (frowny
face).
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