Characteristics of a Parabola in Standard Form. Quadratic Vocabulary Parabola: The graph of a quadratic equation. x-intercept: The value of x when y=0.

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Presentation transcript:

Characteristics of a Parabola in Standard Form

Quadratic Vocabulary Parabola: 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) (-2,0) and (2,0) Opens Down

Investigating a Parabola x = 1 (1,0) (0,1) (1,0) Opens Up x = 2 (2,1) (0,5) None Opens Up 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

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

Quadratic Characteristics The standard form of a quadratic equation (ax 2 +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: Since “a” is negative (-2), the parabola opeds down Since “c” is +7, the y- intercept is (0,7)