Graphing Quadratic Functions

The vertex

(h , k) *(vertex form)

a is negative

If the graph opens down...

standard form

ax^2 + bx + c = 0

Quadratic function

is a function that can be written in standard form

a is positive

If the graph opens up...

1 real solution

Discriminant is equal to 0

2 real solutions

Discriminant is greater than 0

0 real solutions

Discriminant is less than 0

parabola

Every quadratic function has U-shaped graph called a ______

zeros, roots, or x-intercepts

Solutions of quadratic functions can also be called the ______, _______, or ___________

True

T/F Cannot have a negative in the denominator

True

T/F cannot take the square root of a negative number

vertex

The _____ is the lowest point of a parabola that opens up and the highest point of a parabola that opens down

how many soultions

The discriminant will tell you ___ ____ ________ a quadratic equation has

wider, narrower

a also tells which graph will be _______ or ______

up, down

a tells us if the parabola opens __ or ____

minimum, maximum

a tells us if the vertex is a _______ or _________

Vertex Form

f(x) = a(x-h)^2 + k

opens down

if the leading coefficient (a) is negative, the parabola

opens up

if the leading coefficient (a) is positive, the parabola

Discriminant

the expression under the radical sign in the quadratic formula

axis of symmetry

the line passing through the vertex that divides the parabola into two symmetric parts called the _____ __ ________

axis of symmetry

x = opposite of h *(vertex form)