1. Equations & Inequalities

In Exercises 109–114, find the x-intercept(s) of the graph of each equation. Use the x-intercepts to match the equation with its graph. The graphs are shown in [- 10, 10, 1] by [- 10, 10, 1] viewing rectangles and labeled (a) through (f). y = x² - 4x - 5

Solve each equation by the method of your choice. $3x^2-7x+1=0$

Find all values of x satisfying the given conditions. y₁ = - x² + 4x - 2, y₂ = - 3x² + x - 1, and y₁ - y₂ = 0

Find all values of x satisfying the given conditions. y = 5x² + 3x and y = 2

Solve each equation by the method of your choice. 1/(x² - 3x + 2) = 1/(x + 2) + 5/(x² - 4)

Write a quadratic equation in general form whose solution set is {- 3, 5}.

Solve each equation in Exercises 83–108 by the method of your choice. (2x + 3)(x + 4) = 1

Solve the given quadratic equation by factoring. $3x^2+12x=0$

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. x² + 3x

Find all values of x satisfying the given conditions. y₁ = 2x² + 5x - 4, y₂ = - x² + 15x - 10, and y₁ - y₂ = 0

Solve each equation in Exercises 15–34 by the square root property. (x + 2)² = 25

Exercises 73–75 will help you prepare for the material covered in the next section. Multiply: (7 - 3x)(- 2 - 5x)

Find all values of x satisfying the given conditions. y₁ = 2x/(x + 2), y₂ = 3/(x + 4), and y₁ + y₂ = 1

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $x^2+12x$

Solve each equation in Exercises 47–64 by completing the square. $x^2+3x-1=0$