Question

1. which of the following scenarios can be solved by writing a quadratic equation? select all that apply.

□ situations involving squared terms
□ finding the perimeter of an object when the sides are unknown
□ problems with right triangles and the pythagorean theorem
□ finding the area of an object when the sides are unknown

Explanation:

1. Situations involving squared terms: Quadratic equations have a degree of 2 (highest power of the variable is 2), so scenarios with squared terms (e.g., \(x^2\)) can be modeled with quadratic equations.
2. Finding the perimeter of an object when the sides are unknown: Perimeter formulas (e.g., for a rectangle: \(P = 2l + 2w\)) are linear (degree 1), so they do not require quadratic equations.
3. Problems with right triangles and the Pythagorean theorem: The Pythagorean theorem is \(a^2 + b^2 = c^2\), which is a quadratic relationship (squared terms), so these problems can be solved with quadratic equations (or derived from them).
4. Finding the area of an object when the sides are unknown: Area formulas for many shapes (e.g., rectangle: \(A = l \times w\); if one side is expressed in terms of the other, it can lead to a quadratic equation, like \(A = x(x + 3)\) which is quadratic).

Answer:

• situations involving squared terms
• problems with right triangles and the Pythagorean theorem
• finding the area of an object when the sides are unknown