Standard Form Quadratics

Front

What is the standard form of a quadratic equation?

Back

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

Front

What does the coefficient 'a' in a quadratic equation determine?

Back

The coefficient 'a' determines the direction of the parabola's opening: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its direction of opening.

Front

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

Back

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

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers, represented as (-∞, ∞).

Front

What is the range of a quadratic function that opens upwards?

Back

The range is [k, ∞), where k is the y-coordinate of the vertex.

Front

What is the range of a quadratic function that opens downwards?

Back

The range is (-∞, k], where k is the y-coordinate of the vertex.

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

To convert, use the method of completing the square.

Front

What is the significance of the y-intercept in a quadratic equation?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the equation at x = 0.

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.