Quadratic Functions Flashcards
Vertex Form
f(x) = a(x-h)² + k
Standard Form
f(x) = ax² +bx + c
Intercept Form
f(x) = a(x-p)(x-q)
Conic Form
y = 1/4p (x-h)² + k
or
x= 1/4p (y-k)² +h
What does the +/- mean in
y = +/- a [ +/- b (x-h)² ] + k
Reflection in the x-axis
What does a mean in
y = +/- a [ +/- b (x-h)² ] + k
Vertical stretch/shrink
How does the vertical stretch/shrink work?
Stretch by 2 -> *2
Shrink by 1/2 -> *1/2
What does b mean in
y = +/- a [ +/- b (x-h)² ] + k
Horizontal stretch/shrink
What does the (x-h)² mean in
y = +/- a [ +/- b (x-h)² ] + k
Move to the left/right
What does k mean in
y = +/- a [ +/- b (x-h)² ] + k
Move up/down
How does the horizontal stretch work
by 2 -> *1/2
by 1/2 -> *2
(x-h) (x+h)
If it’s neg., move to the…
If it’s pos., move to the…
when using f(x) = a(x-h) +k
Right
Left
How to find the vertex of a function (standard form)
Use x=-b/2a and plug a and b into it
Then plug x into the whole equation
IS the min/max x or y?
Y
How to find the equation of the parabola with the focus and the directrix.
Create a system using
h+p + h-p if directrix is x= d
plug into equation 1/4p(y-k)² +h
or
k+p + k-p if directrix is y=d
Plug into equation
1/4p(x-h)² +k
How to find the equation of a parabola with the vertex and the directrix.
Plug the directrix into the formula (y=k-p or x=h-p) to find the p value.
Plug into equation
y=1/4p(x-h)² +k or x=1/4p(y-h)² + k
How to find the equation of a parabola with the focus and the vertex.
Plus the value of the focus into the formula (h, k+p or h+p, k) to find the p value.
Plug into equation
1/4p(x-h)² +k
What is the vertex for y=1/4p(x-h)² +k
(h, k)
What is the focus for y=1/4p(x-h)² +k
(h, k+p)
What is the directrix for y=1/4p(x-h)² +k
y= k-p
What is the AOS for 1/4p(x-h)² +k
x=h
What is the vertex for 1/4p(y-k)² +h
(h,k)
Does 1/4p(y-k)² +h open left/right or up/down
Left/right
What is the focus for 1/4p(y-k)² +h
(h+p, k)
What is the directrix for 1/4p(y-k)² +h
x= h-p
What is the AOS for 1/4p(y-k)² +h
y=k
