Answer:
Identifying Quadratic Equations
A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
Let's analyze each equation:
Not Quadratic Equations
* 3m + 8 = 15: This is a linear equation, as the highest power of the variable (m) is 1.
* a - 5x + 10 = 0: This equation seems to have two variables (a and x). If we assume 'a' is a constant, then it becomes a linear equation in terms of x.
* 12 - 4x = 0: This is also a linear equation.
* 2² - 7t = 12: This simplifies to -7t = 8, which is a linear equation.
* 25 - 4r: This is not an equation at all, but an expression.
* 3x(x - 2) = -7: Expanding this gives 3x² - 6x = -7, which can be rearranged to 3x² - 6x + 7 = 0. This is a quadratic equation.
* (h - 6) = 0: This is a linear equation.
* (x + 2)² = 0: Expanding this gives x² + 4x + 4 = 0. This is a quadratic equation.
Quadratic Equations
* 6 - 2x + 3x² = 0: This is a quadratic equation in standard form.
* (w - 8)(w + 5) = 14: Expanding this gives w² - 3w - 54 = 0. This is a quadratic equation.
Summary:
* Quadratic equations: 5, 7, 9, 10
* Not quadratic equations: 1, 2, 3, 4, 6, 8
Remember, a quadratic equation must have a term with the variable squared, and no higher powers of the variable.
