Quadratics
What is the shape of the graph of a quadratic function called?
Parabola
What is the name of a letter used as a placeholder for a number?
Variable
Name three different types of functions.
(multiple answers)
What does a linear graph look like?
A straight line
Name one exponential property.
(Multiple Answers)
What are the three forms of a quadratic equation?
Standard, Factored, Vertex
What is the name for a number in front of a variable?
Coefficient
What type of function is this: y=|x-2|2+5 and what is the vertex?
Absolute Value Function
Vertex: (2,5)
What is the equation of a linear function? What do the variables represent?
y=mx+b
m: slope (rise/run)
b: y-intercept
Simplify and solve: 23(22)
25=32
What are the roots of the following quadratic function: y=x2+6x-7
y=(x+7)(x-1)
The roots are x=-7,1
How do we refer to the number 2 in the term x2 ?
Exponent or power
No!
Given the points (-2,1) and (2,9) find the corresponding linear equation.
y=2x+5
What is the inverse function to exponential functions?
Logarithms
What is the vertex of the following quadratic function:
y=x2+4x-8
Vertex form: y=(x+2)2-12
Vertex: (-2,-12)
For polynomials, what do we call the highest power out of all of the terms?
The degree of the polynomial.
Write the equation for a square root function with a vertical stretch of 2 and with vertex (-3,4).
y=2sqrt(x+3)+4
Graph the equation: y=(-2/3)x+1
(check work)
What is the equation for exponential functions?
y=a(bx)
What do we call this type of quadratic:
y=x2-9
Also, what is the rule for these?
Difference of perfect squares.
Rule: y= a2-b2 = (a-b)(a+b)
What is the difference between an expression, an equation and a function?
An expression has terms not set equal to anything.
An equation has terms set equal to another term(s).
A function is an equation with two variables where one variable depends on the other and every input has only one output.
Is the equation of a circle a function? Why or why not?
No because when we graph the equation of a circle, it fails the vertical line test (i.e. some inputs have more than one output).
How do we know two linear functions are parallel? Perpendicular?
Parallel: same slopes, different y-intercepts
Perpendicular: opposite slopes (negation of the reciprocal)
Find an exponential model for the following two points: (0,2) and (3,16)
y=2(2x)