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

By the End of This Section … You will be able to identify key aspects of the graph of a function based on its equation in vertex form, intercept form, and standard form. You will understand the significance of the vertex and that the y-value of the vertex is the maximum or minimum of the function while the x-value is when or where that maximum or minimum occurs.

Properties of Parabolas

First Identify h and k to determine the vertex and axis of symmetry. Second, find another point by picking a value of x close to the axis of symmetry and plugging it in to the function to find the y-value that goes with it. Third, reflect that point over the axis of symmetry and draw the parabola through the three points you have plotted. *** I like to plot a fourth and fifth point whenever possible to have a more accurate graph.

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

Graphing a Quadratic Function in Standard Form

Maximum and Minimum Values

Since we have a minimum value, all of the y values will be at or above that minimum value. All Real Numbers The minimum is -3

Graphing Quadratic Functions Using x-intercepts

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.

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.

Finding a Minimum or Maximum

Graphing Quadratic Functions

Graphing a Quadratic Function in Intercept Form