CHAPTER 8: QUADRATIC FUNCTIONS Flashcards
General Quadratic function
f(x) = ax^2 + bx + c
a is nonzero
quadratic function graph is always a _ shape
parabola
parabola
U-shaped figure that opens with upwards or downwards
when does a parabola open upwards
a>0
when does a parabola open downwards
a<0
y-intercept in quadratic function
c
x-intercepts of quadratic functions
real zeros of f
do quadratic functions have to have 0s?
no
discriminate
b^2-4ac
what are the zeros of f
roots of the quadratic equation
If discriminate is >0, how many roots?
2
If discriminate is = 0, how many roots?
1
If discriminate is <0, how many roots?
0
vertex/standard form of quadratic quesiton
f(x) = a(x-h)^2+k
a is nonzero
How to convert vertex/standard form to general form
completing the square
how to complete the square
if x^2+mx, add (m/2)^2
Quadratic equations in the form x = ay^2 + by + c where a is nonzero do not define functions of x, true or false?
true
if a >0, parabola opens upwards and has a _ point
lowest
if a <0, parabola opens downwards and has a _ point
highest
vertex
highest point of parabola that opens downwards or lowest point of parabola that opens upwards
vertex of f(x) = a(x-h)^2+k
h,k
vertex of f(x)=ax^2+bx+c
-b/2a,f(-b/2a)
axis of symmetry for parabola
vertical line where parabola is symmetric throughout its vertex
absolute maximum value
vertex
absolute minimum value
vertex
vertex is important for finding the
range
