Properties of Quadratics
What are the 3 types of quadratic equations?
Vertex Form, Standard Form, Factored Form
How do we determine if a quadratic has a maximum or minimum?
Maximum if the parabola opens down / Minimum if the parabola opens up
What is an inverse?
Reverse or "undoes" the operations performed by a function.
What is a radical?
A radical is a square, cube, or higher root.
How do we determine the axis of symmetry given a vertex form equation?
By the x or h value of the vertex
How do we find the max/min value in vertex form?
f(x) = a(x-h)² + k
Max/min is the k value, and the a value determines if the k value is a minimum or maximum
How can we find the inverse of a function algebraically?
Switch x and y and then solve for y
Determine if this is an example of an entire or mixed radical.
√42
Entire radical
What information does vertex form tell us?
The vertex x and y coordinate, the vertical stretch, and the reflection on the x-axis.
How do we find the max/min value in standard form?
f(x) = ax² + bx + c
Complete the square to go from standard form to vertex form
How can we find the inverse of a function graphically?
Switch coordinate points (x,y) to (y,x)
Rewrite this mixed radical as an entire radical.
3√7
√63
How do we go from factored form to vertex form?
Expand + complete the square.
How do we find the max/min value in factored form?
f(x) = a(x-r)(x-s)
If the domain and range of a function are: {XER} & {YER|y>=-2}. What would they be for the inverse function?
{XER|x>=-2} & {YER}
Simplify.
√5 + √3 + 2√5 - 4√3
= 3√5 - 3√3
Find the vertex coordinates, direction of opening, and coordinates of the y-intercept.
f(x) = 3(x+1)² - 5
Coordinates of the vertex: (-1,-5)
Direction of opening: up
Coordinates of the y-intercept: (0,-2)
Determine the maximum or minimum value for this quadratic: f(x) = (x-4)(x-6)
minimum is y=-1
Determine the equation of the inverse given this function.
f(x) = 2(x+3)^2-4
y=±√(x+4/2)-3
Simplify.
(2-√3)(1+√6)
= 2 + 2√6 - √3 - 3√2