Unit 2 - Quadratics Flashcards
factor a² - b² - what are the factors called? what method is this?
(a-b)(a+b) - these are conjugates and the method is difference of squares
what do you write if it has no factors?
Prime. Also please don’t unless you’ve tried absolutely everything. Including imaginary solutions.
What is the zero product property?
If A and B are both real or algebraic expressions, if AB = 0, A or B = 0 (at least one - could be both)
What is the domain of a quadratic function?
set of real numbers, (negative infinity, infinity)
When |a| < 1, does the graph get thiccer or thinner (wider or narrower)
thiccer and wider - a smol = thicc graph
Standard form of a parabola
y = ax² + bx + c
Factored/intercept form of a parabola
y=a(x-p)(x-q)
Vertex form of a parabola
y=a(x-h)²+k
Y intercept of standard form parabola
0, f(0)
x intercepts of a standard form parabola
you gotta factor that spit to get there - no easy peasy formula
Axis of symmetry of a standard form parabola
-b/2a
Vertex of a standard form parabola
-b/2a, f(-b/2a)
Range of a standard form parabola
consider y coord of vertex and sign of a, then make a decision
y intercept of a factored form parabola
0, f(0)
x intercepts of a factored form parabola
(p,0) and (q,0) (please remember to make the sign correct)
AoS of a factored form parabola
(p+q)/2
(find the average/midpoint between x intercepts)
Vertex of a factored form parabola
p+q … p+q
____ , f( _______)
2 … 2
y intercept of a vertex form parabola
0, f(0)
x intercepts of a vertex form parabola
this is very annoying because it’s very sneaky about x intercepts and will not tell you in a simple la dee da formula way
axis of symmetry in a vertex form parabola
h (NOT K FOR THE LOVE OF GOD)
vertex of a vertex form parabola
(h,k) that’s why it’s called vertex
how do you convert vertex form to standard form?
square whatever’s in the parentheses
distribute a
add k
add it all up
how do you convert vertex form into factored form?
by putting it into standard form
and then factoring because math would like to give me a personal f u
If the vertex is (2,4) and a point is (1,3), write a parabola in vertex form that contains those points.
y=a(x-2)²+4
3=a(1-2)²+4
3=a+4
a=-1
y=-(x-2)²+4