Question
Describe how to derive the quadratic form
Answers
Answered by
GPT 3.5
To derive the quadratic form, follow these steps:
1. Start with a general quadratic equation in the form of \( ax^2 + bx + c \).
2. Expand the equation by multiplying out the terms: \( a(x^2) + b(x) + c \).
3. Simplify the equation by combining like terms to get the quadratic form: \( ax^2 + bx + c \).
4. The quadratic form can also be expressed as \( a(x-h)^2 + k \), where \( h \) and \( k \) are the coordinates of the vertex of the parabola. This form can be obtained by completing the square on the original quadratic equation.
5. By deriving the quadratic form, you can gain insight into the vertex of the parabola, its direction of opening, and any transformations that have been applied to it.
1. Start with a general quadratic equation in the form of \( ax^2 + bx + c \).
2. Expand the equation by multiplying out the terms: \( a(x^2) + b(x) + c \).
3. Simplify the equation by combining like terms to get the quadratic form: \( ax^2 + bx + c \).
4. The quadratic form can also be expressed as \( a(x-h)^2 + k \), where \( h \) and \( k \) are the coordinates of the vertex of the parabola. This form can be obtained by completing the square on the original quadratic equation.
5. By deriving the quadratic form, you can gain insight into the vertex of the parabola, its direction of opening, and any transformations that have been applied to it.