Podcast
Questions and Answers
What is the vertex form of a quadratic equation?
What is the vertex form of a quadratic equation?
- y = a(x + h)^2 + k
- y = a(x - h)^2 + k (correct)
- y = (x + h)(x - k)
- y = ax^2 + bx + c
What does X equal in the context of a quadratic function?
What does X equal in the context of a quadratic function?
h
What is the standard form of a quadratic equation?
What is the standard form of a quadratic equation?
- y = (x + p)(x + q)
- y = ax + b
- y = a(x - h)^2 + k
- y = ax^2 + bx + c (correct)
What does 'a' represent in the standard form of a quadratic equation?
What does 'a' represent in the standard form of a quadratic equation?
What is the zero of the function?
What is the zero of the function?
What is the process of completing the square?
What is the process of completing the square?
What is the quadratic formula?
What is the quadratic formula?
What does the discriminant represent?
What does the discriminant represent?
If b^2 - 4ac = 0, there is one distinct real solution.
If b^2 - 4ac = 0, there is one distinct real solution.
If b^2 - 4ac > 0, there are two distinct real solutions.
If b^2 - 4ac > 0, there are two distinct real solutions.
If b^2 - 4ac < 0, there are two distinct real solutions.
If b^2 - 4ac < 0, there are two distinct real solutions.
What does the expression 'b^2 - 4ac < 0' represent?
What does the expression 'b^2 - 4ac < 0' represent?
What does the term 'SANDWHICH' refer to?
What does the term 'SANDWHICH' refer to?
Study Notes
Vertex Form and Axis of Symmetry
- The vertex form of a quadratic function is given by ( y = a(x-h)^2 + k ).
- The vertex is represented by the point ( (h, k) ).
- The axis of symmetry of the parabola is defined by the line ( x = h ).
Standard Form and Characteristics
- The standard form of a quadratic function is ( y = ax^2 + bx + c ).
- In this form, ( a ) determines the vertical stretch or shrink of the parabola. A positive ( a ) opens upwards, while a negative ( a ) opens downwards.
Zeros of the Function
- The zeros of the function are the input values that make the output ( f(x) = 0 ).
Completing the Square
- Completing the square involves rewriting a quadratic equation in the form ( x^2 + bx + (b/2)^2 = (x + b/2)^2 ).
Quadratic Formula
- The quadratic formula to find the roots of a quadratic equation is given by ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ).
Discriminant Analysis
- The discriminant, represented by ( b^2 - 4ac ), determines the nature of the roots of the quadratic equation.
- If ( b^2 - 4ac = 0 ), there is one distinct real solution.
- If ( b^2 - 4ac > 0 ), there are two distinct real solutions.
- If ( b^2 - 4ac < 0 ), there are two distinct non-real complex solutions.
General Notes
- Always check the value of the discriminant to identify the types of solutions for quadratic equations.
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Description
This flashcard set covers key concepts from Algebra 2/Trig Chapter 2, including vertex form, axis of symmetry, and standard form of quadratic equations. Enhance your understanding of quadratic functions and their properties with these essential definitions.
