Sec. 11-1 Graphing Quadratic Functions. Graph the following equations on 1 piece of graphing paper y = x + 1 y = 2x + 4.

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Presentation transcript:

Sec Graphing Quadratic Functions

Graph the following equations on 1 piece of graphing paper y = x + 1 y = 2x + 4

Important terms The shape of a _____________ is like an ________. Picture: Parabolas are modeled by ___________ __________ of the form ______________.

Quadratic Function Words: A quadratic function is a function that can be described by an equation of the form ______________ where ______. Models:

Example: Graph the quadratic function by making a table of values. y = x 2 + 1

Graph the quadratic function by making a table of values. y = -x 2

A parabola’s ___________ is its lowest point. A parabola with a _________ coefficient of its quadratic term will have one of these. Example:Picture: A parabolas ____________ is its highest point. A parabola with a _________ coefficient of its quadratic term will have one of these. Example:Picture:

Your Turn! 1. y = x y = -2x 2 - 1

More important terms The maximum or minimum point of a parabola is called the ___________. The vertical line containing the vertex of a parabola is called the ______ ___ _____________. Picture:

Equation for Axis Of Symmetry Determining the Vertex of a Parabola The equation for the axis of symmetry: To determine the vertex of a parabola by plugging in the x value from the line of symmetry and solving for y.

y = x 2 – 4x – 1. A.Find the equation of the axis of symmetry B. Find the coordinates of the vertex of the parabola.

C. Graph the Function.

Use characteristics of quadratic functions to graph y = -x 2 + 2x – 3. A.Find the equation of the axis of symmetry B. Find the coordinates of the vertex of the parabola. C. Graph the Function.

y = -x 2 + 2x – 3. A. Find the equation of the axis of symmetry B. Find the coordinates of the vertex of the parabola.

y = -x 2 + 2x – 3. C. Graph the Function.

A football player throws a short pass. The height y of the ball is given by the equation y = -16x 2 + 8x + 5 where x is the number of seconds after the ball was thrown. What is the maximum height reached by the ball?

If you graph the function for the height of a football it looks like this

HOMEWORK This is a change from the homework board!! Practice 11 – 1 PLUS Worksheet Titled Graphing Quadratic Equations – SIDE 1