Solving for a Variable
Solve for x in the equation \(5x - 2 = 3x + 4\).
Converting from Interval to Inequality
Convert the interval notation \(( -\infty, 3 ]\) to inequality notation.
Solve by Completing the Square
Solve the equation by completing the square: \(x^2 - 6x + 5 = 0\)
Finding the Domain
Find the domain of the function \( f(x) = \frac{1}{\sqrt{5-x}} \)
Finding the Range
Find the range of the function \(y= 2x^2 - 3x + 1\) when \(x\) is in the interval \([-2,3]\).
Finding the Domain and Range
Find the domain and range of the function \( f(x) = \sqrt{4-x} \)
Finding the Asymptotes
Find the vertical and horizontal asymptotes of the function \(y = \frac{2x^2 - 3x + 1}{x - 1}\).
Solving by Factoring
Solve the following equation by factoring: \(x^2 - 5x + 6 = 0\)
Solving Rational Equations
Solve the rational equation \( \frac{x}{x-3} - \frac{2}{x+1} = \frac{1}{x^2-2x-3} \).
Quadratic Formula
Find the roots of the quadratic equation \(3x^2 + 7x - 6 = 0\) using the quadratic formula.
Quadratic Inequalities
Solve the quadratic inequality: \(x^2 - 4x - 5 \leq 0\).
Rational Inequalities
Solve the following rational inequality: \(-\frac{2}{x-3} \geq 1\)
Finding the Discriminant
Find the discriminant of the quadratic equation \(3x^2 - 4x + 2 = 0\)
Finding the Quadratic Constant of Variation
Given the quadratic function \(y = ax^2 + bx + c\) passes through the points (1,7), (2,11), (3,17), determine the constant of variation \(a\).