6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex

A Quadratic function Parts of the Quadratic function. CONSTANT TERM

The graph of a Quadratic function is called a parabola. A Quadratic function

Parabola are Symmetrical Axis of Symmetry, splits it down the middle

Parabola are Symmetrical Points reflect across the axis of symmetry

Parabola are Symmetrical The equation for the axis symmetry is

The y – Intercept of a parabola If x = 0, then c is the y intercept

The Vertex of the Parabola The Vertex is a point at the highest or lowest point of the graph of a parabola. The Vertex is on the axis of symmetry, so its x coordinate is found by

Now that you have x of the Vertex how do you find the y x = 1

How can you tell if the Vertex is the highest or lowest point. It all depends on “a”. If a > 0, the parabola If a<0, the parabola is opens upward.opens downward

The Maximum or Minimum value is the y value of the vertex If the vertex is ( -3, 1), of f(x)= x 2 + 6x + 10, then the minimum value is 1. Since the parabola is opening upward it is the minimum.

How to graph the parabola f(x) = 2- 4x + x 2 Rewrite the function. f(x) = x 2 -4x + 2 Find the y intercept: f(0) = (0) + 2 = 2 (0, 2) Find the vertex: a = 1, b= -4

How to graph the parabola f(x) = 2- 4x + x 2 Start a table using number higher and lower then 2, from the vertex. Plot points

How to graph the parabola f(x) = 2- 4x + x 2 Connects the points.

Graph the function. Show the y intercept, axis of symmetry and vertex f(x) = -x 2 + 2x + 3

Graph the function. Show the y intercept, axis of symmetry and vertex f(x) = -x 2 + 2x + 3 Does the graph open up or down? What are a, b and c?

Graph the function. Show the y intercept, axis of symmetry and vertex f(x) = -x 2 + 2x + 3 Does the graph open up or down?Down What are a, b and c? a = -1 b = 2 c = 3, so the y intercept is (0,3)

Graph the function. Show the y intercept, axis of symmetry and vertex f(x) = -x 2 + 2x + 3 axis of symmetry is x = 1 What are a, b and c? a = -1The vertex is b = 2 c = 3

Graph the function. Show the y intercept, axis of symmetry and vertex f(x) = -x 2 + 2x + 3 Plot the points

Graph the function. Show the y intercept, axis of symmetry and vertex f(x) = -x 2 + 2x + 3 Connect the points

Homework Page 291 # 15, 19, 23, 25, 33 – 43 odd

Homework Page # 16, 22, 26, even, 46, 47