Quadratic Functions (Graphing, Vertex, and Line of symmetry)
what is a quadratic function?
a function that can be written as f(x) = ax 2 + bx + c, where "a" is not zero
What is the solution set of the equation (x + 1)(x - 5) = 0 ?
x = -1 and x = 5
Definition of Linear Function
Function with a constant rate of change whose graph forms a straight line.
what type of equation is this?
f(x) = mx+b
Equation of a linear function
Exponential Function
a function with a variable as the exponent
how do you find the vertex?
Plugin the Axis of Symmetry and write as an ordered pair.
What is the solution set of the equation (x + 1)(x + 2) = 0 ?
x = -1 and x = -2
y = 2x has a y-intercept of...?
0
what type of equation is this?
f(x) = x^2
Equation of a quadratic function
Exponential Growth
an exponential function that INCREASES from left to right
write an equation of the quadratic function with a vertex at (2,-3) which passes through the point (4,1)
y=x-2)^2-3
What is the solution set of the equation (2x + 3)(4x + 3) = 0?
x = -3/2 and x = -3/4
What is the y-intercept if y = -2x - 4?
-4
what type of equation is this?
f(x) = | x |
Equation of an absolute value function
Exponential Decay
an exponential function that DECREASES from left to right
(0,-3)
(3,0)
(-1,0)
The zeros of the function f(x) are -6 and 5. What could be the function?
f(x) = (x + 6)(x - 5)
Is the slope of y = 2x - 3 negative or positive?
positive
what type of equation is this?
f(x) = √x
Equation of a square root function
Horizontal Asymptote
an imaginary, horizontal line that a graph comes really close to, but does not cross
does this parabola open up or down?
y=2x^2+x-1
up
What are the roots of the following equation?
x² - 5x -35 = 3x
x = -7 and x = 5
What is the y-intercept of y = 0.5x + 5?
5
definition of range
All possible y-values for a given function
Initial value
The starting amount or y-intercept of the graph, the "a" part