To determine which of the given options represents a quadratic equation, we need to recall the standard form of a quadratic equation. A quadratic equation is generally of the form:
[tex]\[ ax^2 + bx + c = 0 \][/tex]
where [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] are constants with [tex]\(a \neq 0\)[/tex].
Now let's examine each option:
Option A: [tex]\( x^2 = 25 \)[/tex]
- This equation can be rewritten as [tex]\( x^2 - 25 = 0 \)[/tex], which fits the standard quadratic form where [tex]\(a = 1\)[/tex], [tex]\(b = 0\)[/tex], and [tex]\(c = -25\)[/tex]. Thus, it is a quadratic equation.
Option B: [tex]\( y = \frac{1}{x^2} \)[/tex]
- This equation cannot be rewritten in the standard quadratic form [tex]\( ax^2 + bx + c = 0 \)[/tex]. It involves an inverse square term [tex]\( x^{-2} \)[/tex], not a quadratic one. Thus, it is not a quadratic equation.
Option C: [tex]\( x - 4 = 7 \)[/tex]
- This equation simplifies to [tex]\( x = 11 \)[/tex]. It is a linear equation, not a quadratic equation, as it can be written in the form [tex]\( x = \text{constant} \)[/tex].
Option D: [tex]\( y = 3x + 2 \)[/tex]
- This equation is a linear equation in the form [tex]\( y = mx + c \)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(c\)[/tex] is the y-intercept. Thus, it is not a quadratic equation.
Based on the evaluation, the correct option that is an example of a quadratic equation is:
A. [tex]\( x^2 = 25 \)[/tex]
