Elementary Geometry for College Students (6th Edition)

(a) This is a quadratic equation. (b) This is a not a quadratic equation. (c) This is a quadratic equation. (d) This is a quadratic equation. (e) This is a quadratic equation for $x \geq \frac{1}{2}$ (f) This is a quadratic equation.
A quadratic equation can be written in this form: $ax^2 + bx+c = 0$ where $a,b,$ and $c$ are real numbers and $a \neq 0$ (a) $2x^2-5x+3 = 0$ $a=2, b = -5, c=3$ This is a quadratic equation. (b) $x^2 = x^2+4$ $-4 = 0$ $a=0, b = 0, c=-4$ This is a not a quadratic equation since $a=0$. (c) $x^2 = 4$ $x^2-4 = 0$ $a=1, b = 0, c=-4$ This is a quadratic equation. (d) $\frac{1}{2}x^2-\frac{1}{4}x-\frac{1}{8} = 0$ $a=\frac{1}{2}, b = -\frac{1}{4}, c=-\frac{1}{8}$ This is a quadratic equation. (e) $\sqrt{2x-1} = 3$ $2x-1 = 9$ $(2x-1)^2 = 81$ $4x^2-4x+1 = 81$ $4x^2-4x-80 = 0$ $a=4, b = -4, c=-80$ This is a quadratic equation for $x \geq \frac{1}{2}$ Since the original equation included the term $\sqrt{2x-1}$, we need to restrict the domain to $x \geq \frac{1}{2}$ (f) $(x+1)(x-1) = 15$ $x^2-1 = 15$ $x^2-16 = 0$ $a=1, b = 0, c=-16$ This is a quadratic equation.