Podcast
Questions and Answers
The graph of a quadratic function is non-linear; it is a _____ (U-Shape).
The graph of a quadratic function is non-linear; it is a _____ (U-Shape).
Parabola
The equation of a quadratic function is a ____ polynomial; it includes an ax² term.
The equation of a quadratic function is a ____ polynomial; it includes an ax² term.
quadratic
What is the standard form of a quadratic function?
What is the standard form of a quadratic function?
ax² + bx + c
In standard form, c = the _______.
In standard form, c = the _______.
The vertical fold line that makes the halves of the parabola match is called the ____________.
The vertical fold line that makes the halves of the parabola match is called the ____________.
In standard form, if a > 0 then the vertex is the (minimum/maximum).
In standard form, if a > 0 then the vertex is the (minimum/maximum).
In standard form, if a < 0 then the vertex is the (minimum/maximum).
In standard form, if a < 0 then the vertex is the (minimum/maximum).
Domain is all the ______ values, range is all the _______ values.
Domain is all the ______ values, range is all the _______ values.
The formula for the line of the axis of symmetry is x=___. It is also the x-value of the vertex.
The formula for the line of the axis of symmetry is x=___. It is also the x-value of the vertex.
A parabola must have __ points plotted.
A parabola must have __ points plotted.
The x-intercepts of a function are called ___.
The x-intercepts of a function are called ___.
What is the PARENT function of a quadratic equation?
What is the PARENT function of a quadratic equation?
The opposite of ( )² is ___; they undo each other.
The opposite of ( )² is ___; they undo each other.
The quadratic formula is x = _______.
The quadratic formula is x = _______.
If you only need to see the key features of a parabola and you have time, you can use the _____ method to find the zeros.
If you only need to see the key features of a parabola and you have time, you can use the _____ method to find the zeros.
If the function is factorable, use the _____ method to find the zeros.
If the function is factorable, use the _____ method to find the zeros.
If the function has no 'bx' term, use the _____ method to find the zeros.
If the function has no 'bx' term, use the _____ method to find the zeros.
If the function is not factorable and has a 'bx' term, use the ______ method to find the zeros.
If the function is not factorable and has a 'bx' term, use the ______ method to find the zeros.
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Study Notes
Quadratic Functions Overview
- A quadratic function's graph takes the shape of a parabola, characterized by a U-shape.
- The equation of a quadratic function is a quadratic polynomial, specifically containing an ax² term.
Standard Form of Quadratic Equation
- The standard form of a quadratic function is represented as y = ax² + bx + c.
- In this form, the y-intercept is given by the constant term c.
Key Features of Parabolas
- The axis of symmetry is a vertical fold line where both halves of the parabola are mirror images.
- When a > 0, the vertex represents a minimum, indicating the parabola opens upward.
- Conversely, if a < 0, the vertex is a maximum, with the parabola opening downward.
Domain and Range
- The domain refers to all possible x values, while the range includes all possible y values.
Finding Key Points and Zeros
- The formula for the axis of symmetry, which also gives the x-value of the vertex, is x = -b/2a.
- To effectively plot a parabola, it’s recommended to have 5 points plotted.
- The x-intercepts of a function are referred to as zeros, roots, or solutions.
Parent Function and Operations
- The parent function for quadratic equations is y = x².
- The operation that inverses squaring is the square root (√), as they undo each other.
Methods to Find Zeros
- To see the key features of a parabola, the graphing method can be employed to find zeros.
- If the quadratic function is factorable, the Zero Product Property should be used to find the zeros.
- When the function lacks a bx term, utilize the Square Root Property for finding zeros.
- If the quadratic is not factorable and includes a bx term, apply the Quadratic Formula:
- x = (-b ± √(b² − 4ac)) ÷ 2a*.
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