Algebra II - Parent Functions

linear parent function

y = x

absolute value parent function

y = |x|

quadratic parent function

y = x²

cubic parent function

y = x³

square root parent function

y = squarerootof x

cube root parent function

y = cuberootof x

reciprocal parent function

y = 1/x

exponential parent function

y = 2^x

linear graph

absolute value graph

quadratic graph

cubic graph

square root graph

cube root graph

reciprocal graph

exponential graph

intercept form equation for quadratic function

f(x) = a (x - h)² + k

vertex is at . . .

( h, k )

axis of symmetry

x = h

a is the . . .

stretch factor

y = -squarerootof x

reflected over x - axis

y = squarerootof -x

relfects over y-axis

y = -squarerootof -x

reflects over both, 180 degree rotation

y = [squarerootof x +1]

vertex shifted left 1 unit

y = [squarerootof x] + 1

shifted up 1 unit

y = a|x|

vertical stretch/shrink

y = |x + 1|

shifted left 1 unit

y = |x| + 1

shifted up 1 unit

quadratics: vertex form

y = a ( x - h )² + k

quadratics: intercept form

y = (x - p)(x - q)

quadratics: standard form

y = ax² + bx + c

p and q

the x-intercepts

formula for finding the vertex with standard form

-b / 2a, then sub that answer in for x to find y

c

y-intercept

how to evaluate y in piecewise functions

1. find the equation in which the selected value of x would make the inequality true

2. sub it in to find y

how to write rules for piecewise functions

1. write the equation of the section of the function in slope-intercept form

2. determine when your equation is true and write it as an inequality that starts with x

graphing quadratic inequalities

1. find the vertex and make a table of values based on it (should by symmetrical!)

2. graph (used dashed/solid line depending on inequality symbol)

3. shade either inside or outside the parabola depending on whether y is greater than or less than the function