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 = - (x + 1)² + 4

Solve each equation in Exercises 1 - 14 by factoring. 7 - 7x = (3x + 2)(x - 1)

Compute the discriminant. Then determine the number and type of solutions for the given equation. x² - 3x - 7 = 0

Solve each equation by the method of your choice. √2 x² + 3x - 2√2 = 0

Solve each equation in Exercises 65–74 using the quadratic formula. $3x^2-3x-4=0$

Use specific values for x and y to show that, in general, 1/x + 1/y is not equivalent to 1 / x + y.

Solve each equation by completing the square. $3x^2-12x+11=0$

Solve by completing the square: 2x² – 5x + 1 = 0.

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

In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation. $x^2-4x-5=0$

Solve each equation in Exercises 15–34 by the square root property. $2x^2-5=-55$

Solve each equation by the method of your choice. $(x-3{)}^2-25=0$

Solve each equation in Exercises 65–74 using the quadratic formula. x² + 5x + 3 = 0

Exercises 100–102 will help you prepare for the material covered in the next section. Factor: $x^2-6x+9$

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $x^2+20x$