Characteristics of Quadratic Functions Section 2.2 beginning on page 56.

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Presentation transcript:

Characteristics of Quadratic Functions Section 2.2 beginning on page 56

The Big Ideas In this section we will learn about…. The properties of parabolas o Axis of symmetry o Vertex Finding the maximum and minimum values of a quadratic function o The vertex is the maximum or minimum o The x-value of the vertex is the location of the max/min and the y- value is the max/min. (This is a concept often used in solving real-world problems. ) o The function will be increasing on one side of the vertex and decreasing on the other side of the vertex. Graphing quadratic functions using x-intercepts o The x-intercepts are the values of x that make y=0 o In real-world problems the x-intercepts are often starting and/or ending points.

Core Vocabulary Previously Learned: x-intercept New Vocabulary: Axis of symmetry Standard form Minimum value Maximum value Intercept form

Properties of Parabolas ** This is good info for your notebook

Using Symmetry to Graph a Parabola ** Just list the basic steps in your notebook to refer to when doing similar problems.

Standard Form The y-value of the axis of symmetry is found by plugging this x-value into the original equation.

Standard Form Sound familiar??

Graphing a Quadratic Function in Standard Form

Graphing Quadratic Functions

Maximum and Minimum Values

Finding a Minimum or Maximum Value Since we have a minimum value, all of the y values will be at or above that minimum value. All Real Numbers

Finding a Minimum or Maximum

Graphing Quadratic Functions Using x-intercepts

Graphing a Quadratic Function in Intercept Form Step 1: Identify the x-intercepts. Step 2: Find the coordinates of the vertex. Step 3: Draw a parabola through the vertex and the points where the x-intercepts occur.

Graphing a Quadratic Function in Intercept Form

Modeling With Mathematics We are comparing the maximum heights and the distance the ball traveled. One shot is represented as a graph, and the other as an equation. The graph shows us that the maximum height is …. The graph shows us that the distance travelled is …. The y value of the vertex is the maximum (50,25). 25 yards The difference in the x-values is the distance the ball traveled. (0,0) and (100,0) 100 yards

Modeling With Mathematics Height : 25 yards Distance : 100 yards To find the max height and distance traveled with the equation we can look at the equation in intercept form. Find the x-intercepts…. Identify the distance travelled… Use the x-intercepts to calculate the maximum height … Distance traveled = 80 yards Maximum height = 32 yards The first shot travels further but the second shot travels higher.