𝟏 Name: ______________________ Period:_______ Lesson 1: 7.1 Graphing Quadratic Functions in Standard Form Learning Objective A: What are we going to learn? B: What is a vertex? Vertex means________________________. CFU We will Graph Quadratic Functions in Standard Form by identifying the vertex 𝟏 . Activate Prior Knowledge Find the vertex of y = 2x2 + 8x +6 2. Find the vertex of y = x2 + 4x + 5 Step 1: Identify a and b: Step 1: Identify a and b: Remember a = __ and b = __ a = __ and b = __ Step 2: Find the X. Step 2: Find the X. 𝒙= −𝒃 𝟐𝒂 = −( ) 𝟐( ) = = ___ 𝒙= −𝒃 𝟐𝒂 = −( ) 𝟐( ) = = ___ Step 3: Find the Y: Step 3: Find the Y: y = 2( )2 + 8( ) + 6 Students, you already know how to find the vertex of a parabola. Now, we will learn how to Graph Quadratic Functions in Standard Form. Make Connection y = ( )2 + 4( ) + 5 Step 4: Write the Order Pair: Step 4: Write the Order Pair: The vertex of 𝑦=_____________𝑖𝑠 𝑎𝑡 (__, _ _) The vertex of 𝑦=_____________𝑖𝑠 𝑎𝑡 (__, _ _) 1: The endpoint of a Parabola. Vocabulary Check your answer with your partner! Concept Development A quadratic function has a standard form of y = ________________, where a ≠ 0. Vertex - the lowest (or highest) point of a parabola at (___,___). Zeroes – where the parabola crosses the _______. A parabola can have ___ zeroes, ___ zero, or ___ zeroes. Zeroes are called the ______________ of the quadratic equation. y-intercept – where the parabola crosses the _________. (There will only be one y-intercept.) Axis of symmetry – splits a parabola into two “mirror images” of each other (𝒙= ). CFU: Identify the key terms below on the graph. Word Bank Vertex Zero Zero y-intercept Axis of symmetry 𝟏

_______ a = __ b = __ 𝒙= −𝒃 𝟐𝒂 = −(__) 𝟐(__) = =______ ( , ) a = __ Skill Development Vertex Form Standard Form If a function is not written in the vertex form, you can use a formula 𝐱= −𝒃 𝟐𝒂 to find the x-coordinate of the vertex. Find the Vertex (h, k). Hint: use the formal x=− 𝒃 𝟐𝒂 ,then substitute back to find y. Steps to Graph Quadratic Functions in Standard Form. 1 2 3 4 Graph the vertex point and draw axis of symmetry line. Find two more points left/right of vertex and Graph it. Reflect the graphed points over the axis of symmetry to create two more points and sketch the graph. How did I/you find the Vertex point? How did I/you find two more points? How did I/you reflect the graph? CFU: Pair Share! 1 3 4 Graph the quadratic function: 𝒚=2x2 + 8x + 6. a = __ b = __ Step 1: 𝒙= −𝒃 𝟐𝒂 = −(__) 𝟐(__) = =______ y = 2( )2 + 8( ) + 6 = ___ Step 2: Graph vertex point (__, __). Step 3: Step 4: Reflect the graph Vertex: ( , ) Graph the quadratic function: 𝒚=x2 + 4x + 5. a = __ b = __ 𝒙= −𝒃 𝟐𝒂 = − 𝟐( ) Step 1: = =____ y = ( )2 + 4( ) + 5 = ___ Step 2: Graph vertex point ( , ). Step 3: ( , ) Vertex: _______ ______ Check your answer with your partner! Step 4: Reflect the graph Discussion Why is it important to find additional points before graphing a quadratic function? 𝟐

1 2 𝟑 Using Vertex will help you graph a quadratic function. Relevance If a function is written in the Standard form, you can use ( −𝒃 𝟐𝒂 , f ( −𝒃 𝟐𝒂 ) to find the vertex (h, k) and pick additional two more points to graph the function. 1 Using Vertex will help you graph a quadratic function. Vertex can be useful in graphing a quadratic functions since the vertex is the point where the parabola crosses its axis of symmetry. We look to the left or to the right of the vertex point to get extra points to help us graph the parabola. We already know that, if the coefficient of  𝑥 2  term is negative then the graph opens down (∩) and thus gives us a maximum point. If the coefficient of the 𝑥 2  term is positive, then the graph opens up(∪) and thus gives us a minimum point. 2 Knowing how to find the Vertex will help you do well on tests. Sample Test Question: Axis of symmetry: x=−0.5 y-intercept: -2 Vertex: (0.5, 2.5) Vertex: (−0.5, 2.5) Vertex: (−0.5, -2.5) Vertex: (0.5, -2.5) A. B. D. Graph f(x) = 2x2 + 2x – 2. Label the axis of symmetry, y-intercept, and vertex. Does anyone else have another reason why it is relevant to use algebraic terminology? (Pair-Share) Why is it relevant to use algebraic terminology? You may give me one of my reasons or one of your own. Which reason is more relevant to you? Why? CFU C. Summary Closure What did you learn today about how to Graph Quadratic Functions in Standard Form by identifying the Vertex? (Pair-Share) Today, I learned how to _________________________________________________ _____________________________________________________________________________________________________________________________________. Standard form Vertex Zeroes y-intercept Axis of Symmetry 1 2 3 4 Steps to Graph Quadratic Functions in Standard Form. 𝟑

a = __ b = __ 𝒙= −𝒃 𝟐𝒂 = −(__) 𝟐(__) = =______ y = ) ( , a = __ b = __ Guided/Independent Practice Find the Vertex (h, k). Hint: use the formal x=− 𝒃 𝟐𝒂 ,then substitute back to find y. Steps to Graph Quadratic Functions in Standard Form. 1 2 3 4 Graph the vertex point and draw axis of symmetry line. Find two more points left/right of vertex and Graph it. Reflect the graphed points over the axis of symmetry to create two more points and sketch the graph. Graph the quadratic function: 𝒚=3x2 + 2x + 1. a = __ b = __ 𝒙= −𝒃 𝟐𝒂 = −(__) 𝟐(__) Step 1: = =______ y = Step 2: Graph vertex point (__, __). Step 3: Step 4: Reflect the graph ) Vertex: ( , Graph the quadratic function: 𝒚=2x2 + 8x − 1. a = __ b = __ 𝒙= −𝒃 𝟐𝒂 = −(__) 𝟐(__) Step 1: = =______ y = Step 2: Graph vertex point (__, __). Step 3: Step 4: Reflect the graph Vertex: ( , ) 4

a = __ b = __ 𝒙= −𝒃 𝟐𝒂 = −(__) 𝟐(__) = =______ y = ( , ) a = __ b = __ Independent Practice Graph the quadratic function: 𝒚=3x2 + 2x. a = __ b = __ 𝒙= −𝒃 𝟐𝒂 = −(__) 𝟐(__) Step 1: = =______ y = Step 2: Graph vertex point (__, __). Step 3: Step 4: Reflect the graph Vertex: ( , ) Graph the quadratic function: 𝒚=2x2 − 5x a = __ b = __ 𝒙= −𝒃 𝟐𝒂 = −(__) 𝟐(__) Step 1: = =______ y = Step 2: Graph vertex point (__, __). Step 3: Step 4: Reflect the graph ) Vertex: ( , 𝟓

a = __ b = __ 𝒙= −𝒃 𝟐𝒂 = −(__) 𝟐(__) = =______ y = ( , ) a = __ b = __ Independent Practice Graph the quadratic function: 𝒚=x2 −4x + 5. a = __ b = __ 𝒙= −𝒃 𝟐𝒂 = −(__) 𝟐(__) Step 1: = =______ y = Step 2: Graph vertex point (__, __). Step 3: Step 4: Reflect the graph Vertex: ( , ) Graph the quadratic function: 𝒚=x2 + 2x − 3. a = __ b = __ 𝒙= −𝒃 𝟐𝒂 = −(__) 𝟐(__) Step 1: = =______ y = Step 2: Graph vertex point (__, __). Step 3: Step 4: Reflect the graph Vertex: ( , ) 𝟔