Quadratic Key Features Review

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola.

Front

How do you find the axis of symmetry given the vertex of a parabola?

Back

The axis of symmetry can be found using the x-coordinate of the vertex. If the vertex is (h, k), the axis of symmetry is x = h.

Front

What is the vertex of a parabola?

Back

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

Front

How do you determine the roots of a quadratic equation?

Back

The roots can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a), where ax² + bx + c = 0.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as x increases, the value of the function also increases.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as x increases, the value of the function decreases.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

How can you identify the direction of a parabola?

Back

The direction of a parabola opens upwards if the coefficient 'a' is positive and downwards if 'a' is negative.

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

How do you find the y-intercept of a quadratic function?

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the point (0, c) in the standard form.