Presentation on theme: "9-1 Graphing Quadratic Functions"— Presentation transcript:
1 9-1 Graphing Quadratic Functions I can:find the vertex of a parabola.find the axis of symmetry of a parabolafind the y-intercept of a quadraticfind the domain and range of a quadratgraph a quadratic using its characteristics9-1 Graphing Quadratic Functions
2 Quadratic FunctionA 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.
3 To Graph a Quadratic: Step 5: Connect the points with a smooth curve Step 1: Find the VERTEX𝒙−𝒗𝒂𝒍𝒖𝒆=− 𝒃 𝟐𝒂 , 𝒚−𝒗𝒂𝒍𝒖𝒆=𝒑𝒍𝒖𝒈 𝒊𝒏 𝒙.Step 2: Find the Axis of Symmetry𝒙=− 𝒃 𝟐𝒂 (𝒙−𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒗𝒆𝒓𝒕𝒆𝒙Step 3: Find the 𝒚 – 𝒊𝒏𝒕𝒆𝒓𝒄𝒆𝒑𝒕Plug in 0 for 𝒙Step 4: Use symmetry to find additional pointsPlug in additional 𝒙−𝒗𝒂𝒍𝒖𝒆𝒔 around vertexStep 5: Connect the points with a smooth curve
4 Example 1: Graph each Quadratic equation and state the domain and range.
5 Example 1: Graph each Quadratic equation and state the domain and range. b. 𝑦= −𝑥 2 +6𝑥−2
6 Example 1: Graph each Quadratic equation and state the domain and range.
7 Example 2: Identify the vertex, axis of symmetry, and the y-intercept of each graph. a b.
8 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.
9 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
10 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?