Solving Quadratics

Front

What is the standard form of a quadratic equation?

Back

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

Front

What does the term 'completing the square' mean?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q.

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens.

Front

How do you find the axis of symmetry of a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the standard form of the quadratic equation.

Front

What is the discriminant and what does it indicate?

Back

The discriminant is given by b² - 4ac. It indicates the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero.

Front

What transformation occurs when you change y = x² to y = (x + 3)²?

Back

The graph translates left 3 units.

Front

What transformation occurs when you change y = x² to y = x² + 4?

Back

The graph translates up 4 units.

Front

How do you determine if a quadratic opens upwards or downwards?

Back

A quadratic opens upwards if a > 0 and downwards if a < 0 in the standard form ax² + bx + c.