Quadratic Characteristics

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

What does it mean if a parabola opens upwards?

Back

It has a minimum value at its vertex.

Front

What does it mean if a parabola opens downwards?

Back

It has a maximum value at its vertex.

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax² + bx + c.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph crosses the x-axis, also known as the zeros of the function.

Front

How can you determine if a quadratic has a maximum or minimum value?

Back

If the coefficient 'a' in the quadratic equation is positive, it has a minimum value; if 'a' is negative, it has a maximum value.

Front

What is the axis of symmetry in a parabola?

Back

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

Front

What is the significance of the 'a' value in the quadratic equation?

Back

The 'a' value determines the direction of the parabola (upward or downward) and its width.

Front

What are the roots of a quadratic equation?

Back

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

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.