What is a quadratic
A quadratic is a equation with the highest degree of a term being 2
What is a quadratic function
A function is quadratic if the 2nd differences of a value are constant
Standard from and Vertex Form
Standard
y = ax^2+bx+c
Vertex form
y = a(x - h)^2 + k
What is a parabola
A parabola is a U shaped curve
Axis of symmetry
Where a symmetrical vertical line can be drawn (the X point of the vertex)
Maximum/minimum point
The lowest/highest Y value the parabola will pass though (K)
y coordinate of the vertex
Y intercept
When the parabola passes through the y-axis, when x = 0
X-intercept
When the parabola passes through the X axis, when y = 0, also called the zeros or roots of the equation.
What happens when you replace A with a real number in y = a(x - h)^2 + k
The parabola is either vertically stretched (2, 3, 4) or compressed (1/2, 2/3, 3/4). The original
Vertical translations (how to create)
When you add or subtract a number outside the (x-h)^2 bracket, the parabola moves up or down vertically X units depending on the number of units added/subtracted
Horizontal translations (how to create)
When you subtract or add a number inside the bracket, there is a horizontal translation. If the number is negative (ex. y=(x - 5)^2, the parabola will move to the right by 5 units. If the number is positive the parabola will move to the left five units.
Reflections
If a parabola is multiplied by -1 outside the bracket the parabola is reflected horizontally. If the parabola is multiplied by -1 inside the bracket the parabola is reflected vertically (no change).
y = a(x - h)^2 + k
(what is each individual symbol)
Axis of symmetry, x = h
Vertex = ( h, k)
Congruent to meaning
The parabola is the same shape as which equation (only vertical stretching/compression)
y = ax^2
How to get A in an equation
If you have the vertex and one point of the graph, you can substitute h and k, and then substitute x and y in order to find A.
What is a function
a function is when for every x coordinate there is only 1 y coordinate
