Quadratic Functions

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About Course

This course provides a complete and practical understanding of quadratic functions, one of the most essential topics in algebra and standardized tests such as the SAT, EST, and ACT. Through clear explanations, visual demonstrations, and real-world examples, students will develop a deep comprehension of how quadratic functions behave, how to represent them in different forms, and how to apply them effectively in problem-solving situations.

Students will learn to analyze, graph, and solve quadratic equations using multiple methods — including factoring, completing the square, and the quadratic formula — and understand the connection between algebraic and graphical representations. Real-world applications such as projectile motion and optimization will help reinforce understanding through meaningful context.

The course also includes targeted Real Test Practice Skills, focusing on how to recognize, simplify, and solve quadratic problems quickly and accurately in test settings.

102 Examples with full explanations and 55 Questions – 7 Quizzes

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What Will You Learn?

  • 1. Understand the concept and properties of quadratic functions, including degree, leading coefficient, and constant term.
  • 2. Identify the vertex, axis of symmetry, intercepts, minimum or maximum values, and direction of opening of a parabola.
  • 3. Represent quadratic functions in multiple forms — standard, vertex, and factored — and convert between them.
  • 4. Solve quadratic equations using factoring, completing the square, and the quadratic formula.
  • 5. Analyze the discriminant to determine the number and nature of the roots.
  • 6. Apply quadratic models to real-world situations, including motion, area, and profit problems.
  • 7. Develop exam-oriented strategies for SAT/EST/ACT questions involving quadratic functions.
  • 8. How to use Desmos and Scientific Calculator.
  • 102 Examples with full explanations.
  • 55 Questions - 7 Quizzes

Course Content

Quadratic Functions
This lessons introduces students to quadratic functions, one of the most important types of nonlinear functions in mathematics. Students will explore the standard form [ f(x) = ax^2 + bx + c ] and learn how to identify key features of their graphs, known as parabolas.Through guided examples and practice problems, learners will: • Understand the shape and direction of parabolas based on the coefficient a. • Find and interpret the vertex, axis of symmetry, x-intercepts (zeros), and y-intercept. • Convert between standard form, vertex form, and factored form of a quadratic function. • Apply methods such as factoring, completing the square, and the quadratic formula to solve quadratic equations. • Analyze real-world situations modeled by quadratic functions, such as projectile motion and area problems. By the end of this lessons, students will be able to graph, interpret, and solve quadratic functions confidently and connect algebraic representations with their geometric meaning.

  • Understand the concept and properties of quadratic functions. its degree, leading coefficient, and constant term.
    20:27
  • Quiz 1
  • Identify the vertex, axis of symmetry, mim. or max. value and vertical intercept.
    35:34
  • Quiz.2
  • Solve quadratic equations using various methods. Number of solutions.
    01:08:40
  • Quiz.3
  • Represent quadratic functions in multiple forms (standard, factored, vertex).
    23:35
  • Quiz.4
  • Analyze the graph of a quadratic function and apply real-world applications.
    31:12
  • Quiz.5
  • Desmos and Calculator Skills.
    29:15
  • Quiz.6
  • Level Up.
    41:40
  • Quiz.7
  • Ready for More? 📚
    00:49

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