Comparing And Contrasting Linear Functions & Quadratic Functions
A quadratic function is any function that canbe written in the form y=ax^2+bx+c
In quadratic functions, the graph is a parabolawhich is U shaped^^^
Parabola 's have an axis of symmetry (dividesthe parabola in two halves. The formula tofind the A.O.S is b/2a.
In the example: y=3x^26x+1, the 3 would bethe 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 orlowest point. To find the vertex, you first haveto find the A.O.S (which is the x value). Thensubstitute that to find the y and that 's how youget 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 (frownyface).
A quadratic function is similar to alinear function by...
Both graphs on a line
Both used in our daily activities
Linear: Walking at a normal pace.... since youare walking at a normal pace your ability towalk more will increase (over time)
Quadratic: When you are doing yourhomework for a long time... if you are doingyour homework for a long time, you will mostlikely get bored and do something else
The equation of a linear function is y=mx=b
A function that is a straight line on agraph
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) asshown above.
Or even negative slopes(decreasing) in linearfunctions
An example of not a linear function may bey^2=0. This not an example of a linearfunction because it is not is slopeinterceptform as above. ^^^^
An example of a linear function are these stairs.As you go up the stairs the slope (in a linearfunction) increases
Another one is this seesaw because it is atan angle
Comparing And Contrasting Linear Functions and Quadratic Functions