Question

Match the forms of a quadratic to its description.(3 points)

Standard Form
Factored Form
Vertex Form

Answer 1

Here are descriptions matched with the forms of a quadratic:

1. **Standard Form**: \( ax^2 + bx + c \)
- This form is used to easily identify the coefficients of the quadratic equation and can be used to find the x-intercepts with some manipulation.

2. **Factored Form**: \( a(x - r_1)(x - r_2) \)
- This form expresses the quadratic as a product of its linear factors, where \( r_1 \) and \( r_2 \) are the roots or x-intercepts of the quadratic.

3. **Vertex Form**: \( a(x - h)^2 + k \)
- This form is useful for identifying the vertex of the parabola directly, where \((h, k)\) is the vertex, and it clearly shows the effect of vertical and horizontal shifts on the graph of the quadratic.

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