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Level 319

Graphing Quadratic Functions


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Quadratic Function
a function that can be written in the form f(x)=ax^2+bx+c, where a, b & c are real numbers and a is not equal to zero
Parabola
the graph of a quadratic function
vertex
The point where two sides meet. (Shared end points of the line segments of a polygon.)
Axis of Symmetry
a line that divides a parabola in two equal halves and goes through the vertex
Domain
The ______________________ is all the possible INPUT, X, values.
Range
The difference between the greatest number and the least number in a set of data.
vertical shrink
the parabola appears wider when y= ax^2 and the absolute value of a is less than 1
vertical stretch
the parabola appears narrower when y= ax^2 and the absolute value of a is greater than 1
Zero Of a Function
for the function f, any number x such that f(x) = 0; an
translation
It is a transformation that moves points the distance and in the same direction.
Maximum Value
The highest point of a parabola ( when a<0)
Minimum Value
The lowest point of a parabola (when a>0)
independent variable
the tested varaible
dependent variable
the measure of change in the independent variable
Even Function
graph is symmetrical with respect to the y-axis; f(x) = f(-x)
Odd Function
graph is symmetrical with respect to both the x-axis and y-axis; f(-x)=-f(x)
vertex form of a quadratic function
a quadratic function in the form y=a(x-h)^2+k where a≠0
intercept form
a quadratic function written in the form f=a(x-p)(x-q), where a does not equal 0
average rate of change
for nonlinear functions, you can compare over the same interval using the slope of the line through (a, f(a)) and
slope
a measure of the steepness of a line; given two points with coordinates (x1,y1) and (x2,y2) on a line