Bell Work Draw a smile Draw a frown Draw something symmetrical.

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Presentation transcript:

Bell Work Draw a smile Draw a frown Draw something symmetrical

Lesson 9.1 Finding the Vertex and Axis of Symmetry for a Parabola

Parabola The shape of a quadratic function.

Parabolas throughout the world

Draw Draw or list 2 real life examples of parabolas

Axis of Symmetry Intersects the parabola at only one point. A line that cuts the parabola in half. Find equation

Vertex The point where the axis of symmetry intersects a parabola A vertex is either a maximum or a minimum of a parabola.

This Parabola has a minimum.

This Parabola has a maximum.

Finding the Vertex and Axis of Symmetry using a Graph.

What is the Vertex of the parabola. What is the Axis of Symmetry What is the Vertex of the parabola? What is the Axis of Symmetry? Is it a Max or min?

Bell Work Axis of Symmetry: Axis of Symmetry: Vertex: Vertex: Min or Max? Axis of Symmetry: Vertex: Min or Max?

Finding Vertex and A.O.S. algebraically 9.2 Finding Vertex and A.O.S. algebraically

Quadratic Function f(x) = ax2 + bx + c A nonlinear function The form above is called standard form

Parabola The shape of a quadratic function.

Standard Form: ax2 + bx + c What if “a” is positive? The parabola has a minimum - or the parabola has a “smiley” face What if “a” is negative? The parabola has a maximum - or the parabola has a “frowny” face

Finding the vertex using the equation y = x2 - 2x - 5 STEP 1: Determine “a”, “b”, and “c” a = 1 b = -2 c = -5

Finding the vertex using the equation y = x2 - 2x - 5 STEP 2: Find the axis of symmetry using x = (-b/2a)

Finding the vertex using the equation y = x2 - 2x - 5 STEP 3: Plug x value back into original equation to solve for y. x = 1 y = (1)2 - 2(1) - 5 = 1 - 2 - 5 = -6 Vertex = (1, -6)