7.
Quadratic formula Method:
Step 1: begin with standard form 𝑎𝑥 # + 𝑏𝑥 + 𝑐 = 0
Step 2: Identify a, b and c from the previous equation (please make sure that you don’t miss sign)
Step 3: Plug in a, b and c in the following formula
−𝑏 ± √𝑏# − 4𝑎𝑐
𝑥=
2𝑎
Step 4: simplify numbers under the square root, multiply 2a in denominator and simplify. Two
answers because two signs in between.
8.Graph Quadratic equation:
Step 1: begin with standard form 𝑎𝑥 # + 𝑏𝑥 + 𝑐 = 0
Step 2: Identify a, b and c from the previous equation (please make sure that you don’t miss sign)
Step 3: Vertex has two coordinates (x , y)
/
Step 4: x coordinate of the vertex is 𝑥 = − #0
Step 5: Identify values for a,b and c from previous step. Make sure that you include the signs
Step 6: Substitute a, b values in the above formula. Simplify the fraction to the lowest term
Step 7: Substitute back x value (from last step) in equation 𝑦 = 𝑎𝑥 # + 𝑏𝑥 + 𝑐 to get y coordinate of
vertex.
/
Step 8: Use axis of symmetry 𝑥 = − #0 and draw a vertical line passing through the vertex.
Step 9: To find x intercepts, Plug in a, b and c in the following formula
−𝑏 ± √𝑏# − 4𝑎𝑐
𝑥=
2𝑎
Step 10: simplify numbers under the square root, multiply 2a in denominator and simplify. Two
answers because two signs in between. These are the x intercepts plot it on the graph.
Step 11: To find y intercepts, Just replace all x in 𝑦 = 𝑎𝑥 # + 𝑏𝑥 + 𝑐 by 0 and solve for y.
Step 12: Plot vertex, x intercepts, y intercepts. You can additionally add points on either side of
vertex along with its corresponding y coordinates to make graph accurate. Connect all the plotted
points.
Wrap Up:
Review Main Concepts:
• Define Standard form, vertex form, axis of symmetry, factorization, complete the square
method, quadratic formula
• Identify and graph quadratic equation
• Interpret the vertex and axis of symmetry, x and y intercepts
• Check with students understanding and queries, addressing common errors
• Quick assessment with lead questions on solving quadratic equation and sketching graph.
• Assessment and Homework.
Lesson review:
Standard form: 𝑎𝑥 # + 𝑏𝑥 + 𝑐 = 0
Key Features: Vertex, axis of symmetry, x intercept and y intercept.
Graph: Plot the graph. Identify axis of symmetry, vertex.
Solving Methods: Factorization, Complete the square, Quadratic formula
Lesson Vocabulary Words:
• Quadratic expression
• Quadratic equation
• Vertex
• Axis of symmetry
• Parabola
• Standard form
• Vertex form
• Factorization
• Coefficient
• Roots
• Discriminant
• Zeroes/Roots
• Intercept
• Completing the square
• Quadratic formula
• Maximum value
• Minimum value
• Graph transformations
• parabola
• Opening of the parabola
Project:
• Investigate real world applications
• Create a visual model of graph
• Use various quadratic equations with its parent graph to describe the shapes and
transformation.
• Role of quadratic equation in sports (like projectile, throwing ball). Gather data and create
table and graph from few rounds in sports
• Compare y=x^2 with quadratic equations taking 5 sets of a,b and c
• Group discussion
Forums:
• What is standard form of quadratic equation?
• What are the key features in graphing quadratic equation?
• Graph transformation in quadratic equation
• What is factorization?
• How to complete the square?
• How to apply quadratic formula?
• How does a, b and c in quadratic equation effects? https://www.desmos.com/calculator
• Compare the methods to factorize quadratic equations
• Discriminant and the types of solutions
• Real world application of quadratic equations
• How to use multimedia in this topic? https://www.geogebra.org/m/TDyefgp6
