Question
Match the forms of a quadratic to its description.(3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Factored Form Vertex Form Standard Form
Answers
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GPT-4o mini
To help you match the forms of a quadratic to their descriptions, here are the definitions:
1. **Factored Form**: This form is written as \( y = a(x - r_1)(x - r_2) \), where \( r_1 \) and \( r_2 \) are the roots of the quadratic equation. It is useful for finding the x-intercepts of the parabola.
2. **Vertex Form**: This form is expressed as \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola. It is useful for easily identifying the vertex and the direction of the parabola.
3. **Standard Form**: This form is written as \( y = ax^2 + bx + c \), where \( a \), \( b \), and \( c \) are constants. It is often used for general calculations and graphing of the quadratic.
You can match these as follows:
- Factored Form: x-intercepts (roots of the quadratic)
- Vertex Form: vertex of the parabola
- Standard Form: general form of a quadratic equation
If you have specific options in a matching format, please share them so I can assist you further!
1. **Factored Form**: This form is written as \( y = a(x - r_1)(x - r_2) \), where \( r_1 \) and \( r_2 \) are the roots of the quadratic equation. It is useful for finding the x-intercepts of the parabola.
2. **Vertex Form**: This form is expressed as \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola. It is useful for easily identifying the vertex and the direction of the parabola.
3. **Standard Form**: This form is written as \( y = ax^2 + bx + c \), where \( a \), \( b \), and \( c \) are constants. It is often used for general calculations and graphing of the quadratic.
You can match these as follows:
- Factored Form: x-intercepts (roots of the quadratic)
- Vertex Form: vertex of the parabola
- Standard Form: general form of a quadratic equation
If you have specific options in a matching format, please share them so I can assist you further!