Key Characteristics of Quadratics

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the quadratic function crosses the x-axis, represented as (x, 0).

Front

What is the axis of symmetry in a quadratic function?

Back

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

Front

How do you find the vertex of a parabola given the equation y = a(x - h)² + k?

Back

The vertex is the point (h, k) where the parabola reaches its maximum or minimum value.

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax² + bx + c, where a, b, and c are constants.

Front

What does the 'a' value in a quadratic equation indicate about the parabola?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width.

Front

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

Back

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

Front

How can you determine the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex, calculated using the formula k in the vertex form y = a(x - h)² + k.

Front

What is the vertex of the parabola given by the equation y = (x + 5)² - 4?

Back

The vertex is (-5, -4).

Front

What is the formula for finding the axis of symmetry of a quadratic function in standard form?

Back

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

Front

What are the characteristics of a parabola that opens upwards?

Back

A parabola that opens upwards has a minimum point at the vertex and the arms extend upwards.