Solving Quadratics by Completing the Square and Quadratic Formula

Front

What is the first step to solving the equation a² + 10a + 21 = 0 by completing the square?

Back

Subtract 21 from both sides.

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.

Front

How do you convert the equation y = x² - 2x - 5 into vertex form?

Back

Complete the square to get y = (x-1)² - 6.

Front

What does the plus or minus symbol (±) indicate in solving quadratics?

Back

It indicates two possible solutions after taking the square root.

Front

What is the quadratic formula?

Back

x = (-b ± √(b² - 4ac)) / (2a) for the equation ax² + bx + c = 0.

Front

What is the purpose of completing the square?

Back

To convert a quadratic equation into vertex form and easily identify the vertex.

Front

What is the vertex of the parabola represented by y = 1/3(x-9)² - 29?

Back

The vertex is (9, -29).

Front

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

Back

The axis of symmetry is x = -b/(2a) from the standard form ax² + bx + c.

Front

What is the significance of the discriminant (b² - 4ac)?

Back

It determines the nature of the roots: two real roots, one real root, or no real roots.

Front

What is the first step in solving a quadratic equation by the quadratic formula?

Back

Identify the coefficients a, b, and c from the equation.