Unit 2 Summary- Non-linear equations

Here is just a brief outline of this unit.

x- linear
x^2- quadratic(one curve)
x^3- cubic(two curves)
x^4- quartic(three curves)
x^5- quintic(four curves)

Standard form
y=ax^2+bx+c

Vertex opening form
y-k=a(x-h)^2
Where (h,k) are the vertex coordinates.

In this equation, the value of "a" tells us the opening.
If a>0, parabola opens up
a<0, opens down
a=1, standard
a>1, narrow
a<1, wide

Parabola with a minimum value is "cup" shaped.
Parabola with a maximum value is "cap" shaped.

Domain= all values of x
Range= all values of y

Axis of symmetry- # of x-axis that passes exactly through to vertex

Cubic function- has no absolute min or max value, only has relative values.

Zeros- were lines passes through x-axis

Non Linear Functions Unit Summary

In this unit summary, we learned about Non Linear Functions.

Quadratic functions can be seen in two different forms...
standard form: y=ax^2 + bx +c
vertex opening form: y - k = a (x - h)^2

In vertex opening form, the a value tells us opening.
If a>0, parabola opens up.
If a<0,>1, parabola is narrow.
If a= <1,>

Ex) y - k = a (x - h)^2
y - 1 = 2 (x + 2)^2
y - 1 = 2 (x - (-2)) ^2
Answer: (h, k) = (-2, 1)

Cubic functions can also be seen in two different forms...
standard form: ax^3 + bx^2 + cx + d = 0
function form: f(x) = ax^3 + bx^2 + cx +d

A cubic equation can have no exponent larger than 3.

Exponential functions are all in the form y = ab^x. Generally, we see exponential graphs look like this...

To solve a basic exponential problem we have to create lists on our calculator and use ExpReg to sove the equation.