9-1 Graphing Quadratic Functions I can: find the vertex of a parabola. find the axis of symmetry of a parabola find the y-intercept of a quadratic find the domain and range of a quadrat graph a quadratic using its characteristics 9-1 Graphing Quadratic Functions

Quadratic Function A quadratic function can be written in the standard form 𝒂 𝒙 𝟐 +𝒃𝒙+𝒄 where 𝑎≠0. The shape of the graph of a quadratic is called a parabola. Parabolas are symmetric about a central line called the axis of symmetry. The axis of symmetry intersects a parabola at only one point, called the vertex.

To Graph a Quadratic: Step 5: Connect the points with a smooth curve Step 1: Find the VERTEX 𝒙−𝒗𝒂𝒍𝒖𝒆=− 𝒃 𝟐𝒂 , 𝒚−𝒗𝒂𝒍𝒖𝒆=𝒑𝒍𝒖𝒈 𝒊𝒏 𝒙. Step 2: Find the Axis of Symmetry 𝒙=− 𝒃 𝟐𝒂 (𝒙−𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒗𝒆𝒓𝒕𝒆𝒙 Step 3: Find the 𝒚 – 𝒊𝒏𝒕𝒆𝒓𝒄𝒆𝒑𝒕 Plug in 0 for 𝒙 Step 4: Use symmetry to find additional points Plug in additional 𝒙−𝒗𝒂𝒍𝒖𝒆𝒔 around vertex Step 5: Connect the points with a smooth curve

Example 1: Graph each Quadratic equation and state the domain and range.

Example 1: Graph each Quadratic equation and state the domain and range. b. 𝑦= −𝑥 2 +6𝑥−2

Example 1: Graph each Quadratic equation and state the domain and range.

Example 2: Identify the vertex, axis of symmetry, and the y-intercept of each graph. a. b.

Maximum and Minimum Values: When 𝒂>𝟎, the graph of 𝑦=𝑎 𝑥 2 +𝑏𝑥+𝑐 opens upward. The lowest point on the graph is the minimum. When 𝒂<𝟎, the graph of 𝑦=𝑎 𝑥 2 +𝑏𝑥+𝑐 opens downward. The highest point on the graph is the maximum.

Example 3: Determine whether the function has a minimum or maximum value and then state the value. a. 𝑓 𝑥 =2 𝑥 2 −4𝑥−1 b. 𝑓 𝑥 =− 𝑥 2 −2𝑥−2

At what height was the T-Shirt launched? Example 4: The cheerleaders at Lake high School launch T-shirts into the crowd every time the Lakers score a touchdown. The height of the T-shirt can be modeled by the function ℎ 𝑥 =−16 𝑥 2 +48𝑥+6, where ℎ(𝑥) represents the height in feet of the T-Shirt after 𝑥 seconds. Graph the function: At what height was the T-Shirt launched? What is the maximum height? When was the maximum height reached?

Homework 9.1 Pages 549-551: 5 – 12, 17 – 20, 45, 46, 63