Quadratics ~ Completing the Square Method

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants, and a ≠ 0.

Front

What does it mean to 'complete the square'?

Back

Completing the square is a method used to convert a quadratic equation into a perfect square trinomial, making it easier to solve.

Front

What is the formula for completing the square?

Back

To complete the square for ax² + bx, take (b/2)² and add it to both sides of the equation.

Front

How do you find the vertex of a parabola from a quadratic equation?

Back

The vertex can be found using the formula (-b/2a, f(-b/2a)) where f(x) is the quadratic function.

Front

What is the significance of the 'b' value in a quadratic equation?

Back

The 'b' value affects the position of the vertex and the direction of the parabola's opening.

Front

What is the first step in completing the square for the equation x² + 6x + 5 = 0?

Back

Move the constant term to the other side: x² + 6x = -5.

Front

What do you do to the 'b' value to correctly complete the square?

Back

Divide by it 2, square the result, then add the result to both sides.

Front

What is the completed square form of the equation x² + 4x?

Back

(x + 2)² - 4.

Front

How can you check if you completed the square correctly?

Back

Expand the completed square form and see if it matches the original quadratic equation.

Front

What is the relationship between the roots of a quadratic equation and its graph?

Back

The roots are the x-intercepts of the graph of the quadratic function.