Characteristics of a Parabola in Standard Form

Quadratic VocabularyParabola: The graph of a quadratic equation.

x-intercept: The value of x when y=0.

y-intercept: The value of y when x=0.

Line of Symmetry: The imaginary line where you could fold the image and both havles match exactly.

Parabola Opens Up: Resembles “valley” OR holds water.

Parabola Opens Down: Resembles “hill” OR spills water.

Vertex: The lowest point of a parabola that opens up and the highest point of a parabola that opens down.

Investigating a Parabola

x = 1

Line of Symmetry:Vertex:y–intercept(s): x–intercept(s):Shape:

x = 1(1,-9)

(0,-8)(-2,0) and (4,0)

Opens Up

x = 0

Line of Symmetry:Vertex:y–intercept(s): x–intercept(s):Shape:

x = 0(0,4)

(0,4)(-2,0) and (2,0)

Opens Down

y x 2 2x 8

y x 2 4

Investigating a Parabola

x = 1

x = 1(1,0)

(0,1)(1,0)

Opens Up

x = 2

x = 2(2,1)

(0,5)None

Opens Up

y x 2 2x 1

y x 2 4x 5

Line of Symmetry:Vertex:y–intercept(s): x–intercept(s):Shape:

Line of Symmetry:Vertex:y–intercept(s): x–intercept(s):Shape:

Investigating a Parabola

x = 3

Line of Symmetry:Vertex:y–intercept(s): x–intercept(s):Shape:

x = 3(3,-4)

(0,5)(1,0) and (5,0)

Opens Up

x = 1.5

Line of Symmetry:Vertex:y–intercept(s): x–intercept(s):Shape:

x = 1.5(1.5,~6.25)

(0,4)(-1,0) and (4,0)

Opens Down

y x 2 6x 5

y x 2 3x 4

Investigating a Parabola

x = 1

Line of Symmetry:Vertex:y–intercept(s): x–intercept(s):Shape:

x = 1(1,0)

(0,-1)(1,0)

Opens Down

x = -2.5

Line of Symmetry:Vertex:y–intercept(s): x–intercept(s):Shape:

x = -2.5(-2.5,~ -5.25)

(0,1)(~ -4.75,0) & (~ -.25,0)

Opens Up

y x 2 2x 1

y x 2 5x 1

Quadratic CharacteristicsThe standard form of a quadratic equation (ax2+bx+c) has

the following connections to the graph:

Does it open up or down?If a is positive, the parabola opens up and the vertex is a

minimum. If a is negative, the parabola opens down and the vertex is a maximum.

What is the y-intercept?c represents the y-intercept ( 0, c )

Example:22 11 7y x x Since “a” is negative (-2), the parabola opeds down

Since “c” is +7, the y-intercept is (0,7)