Everything QUADRATICS

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers.

Front

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

Back

The range is y ≥ k, where k is the minimum value (the vertex).

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point on the graph of a quadratic function.

Front

What does the axis of symmetry represent in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves.

Front

How do you find the axis of symmetry for the quadratic function y = ax^2 + bx + c?

Back

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

Front

What is a y-intercept in the context of a quadratic function?

Back

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

Front

What is an x-intercept in a quadratic function?

Back

The x-intercepts are the points where the graph intersects the x-axis, found by solving the equation y = 0.

Front

What is the standard form of a quadratic function?

Back

The standard form is y = ax^2 + bx + c, where a, b, and c are constants.

Front

What does the 'a' value in a quadratic function indicate?

Back

The 'a' value indicates the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.