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 first step in completing the square for the equation x² + bx?

Back

The first step is to take the coefficient of x (which is b), divide it by 2, and square the result.

Front

How do you find the value to add when completing the square?

Back

Take (b/2)² and add it to both sides of the equation.

Front

What is the completed square form of the equation x² + 6x?

Back

The completed square form is (x + 3)² - 9.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How do you convert from standard form to vertex form?

Back

You can convert by completing the square on the standard form equation.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

What happens to the graph of a quadratic function when 'a' is positive?

Back

When 'a' is positive, the parabola opens upwards.

Front

What happens to the graph of a quadratic function when 'a' is negative?

Back

When 'a' is negative, the parabola opens downwards.