Solving quadratics

Front

What is the first step in solving the quadratic equation x² + 6x - 13 = 3?

Back

Make it equal 0 by subtracting 3 on each side.

Front

How many types of solutions can a quadratic equation have?

Back

A quadratic equation can have one real solution, two real solutions, or two nonreal (imaginary) solutions.

Front

What is the factored form of x² - 4x + 4 = 20? Fill in the blank: (x - __)² = 20

Back

2

Front

What are the solutions to the equation 7x² + 1 = 8?

Back

± 1

Front

Complete the square for x² + 12x + ____. What goes in the blank?

Back

36

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants.

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if > 0, two real solutions; if = 0, one real solution; if < 0, two nonreal solutions.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you find the axis of symmetry for a quadratic equation in standard form?

Back

The axis of symmetry is given by the formula x = -b/(2a).

Front

What is the process of completing the square?

Back

Completing the square involves rewriting a quadratic in the form x² + bx as (x + b/2)² - (b/2)².