Characteristics of Quadratics
domain
All x values (input values) of the parabola.
range
All y values (output values) of the parabola.
maximum/down
Does this parabola have a maximum or minimum? Does it open up or down?
down
Does this parabola open up or down?
up
Does this parabola open up or down?
vertex
The point at which a parabola crosses its axis of symmetry.
Roots/ X-intercepts
The points at which a parabola crosses the x-axis. Each quadratic equation will have 2, 1, or zero roots.
ax²+bx+c
standard form of a quadratic equation.
all real numbers
the domain of a parabola
axis of symmetry
the line through the parabola so that each side is a mirror image of each other.
minimum
when the vertex is the lowest point of a parabola.
parabola
U-shaped graph that represents a quadratic function.
none; this parabola does not cross the x-axis therefore it has no real solutions.
What are the roots, zeros, x-intercepts, or solutions of this function?
{-1, 1/2}
What are the roots, zeros, x-intercepts, or solutions of this function?
{0, -4}
What are the roots, zeros, x-intercepts, or solutions of this function?
{1, 3}
What are the roots, zeros, x-intercepts, or solutions of this function?
{3} - only one root
What are the roots, zeros, x-intercepts, or solutions of this function?
x = -2
What is the axis of symmetry?
x = 0
What is the axis of symmetry?
x = 2
What is the axis of symmetry?
x = 3
What is the axis of symmetry?
( -2 , 4 )
What is the vertex?
( 0 , 3 )
What is the vertex?
( 2 , 1 )
What is the vertex?
( 3 , 0 )
What is the vertex?
maximum
When the vertex is the highest point of a parabola.