Solving Quadratic Equations

A chemist is studying the reaction of $H_{2}$ and $O_{2}$ to form $H_{2}O$. If the equation can be modeled by $x^{2} - 5x + 6 = 0$, what are the values of $x$ that satisfy this equation?

In a chemical reaction, the rate can be modeled by the quadratic equation $R(x) = 2x^{2} - 8x + 6$. What is the maximum rate of reaction?

If the pH of a solution is modeled by the equation $pH(x) = 3x^{2} - 12x + 9$, what are the roots of this equation?

A quadratic equation representing the concentration of a reactant is given by $C(x) = x^{2} - 4x + 4$. What is the concentration at $x = 4$?

For a specific reaction, the yield can be modeled by the equation $Y(x) = -x^{2} + 6x - 8$. What is the yield when $x = 3$?

A chemical engineer models the temperature change with the equation $T(x) = x^{2} - 6x + 9$. What is the vertex of this parabola?

In a reaction, the volume $V$ is represented by the equation $V(x) = x^{2} + 4x - 12$. What are the roots of the equation?

A scientist derives an equation for the pressure of a gas given by $P(x) = -2x^{2} + 12x - 10$. What is the maximum pressure?

The reaction rate can be modeled by the equation $R(x) = 4x^{2} - 16x + 15$. What are the x-intercepts of this quadratic?

A quadratic equation for a chemical equilibrium is given by $K(x) = x^{2} - 10x + 21$. What are the equilibrium points?