Axis of Symmetry

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. It passes through the vertex.

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), where a and b are coefficients from the quadratic equation ax^2 + bx + c.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It is the point where the axis of symmetry intersects the parabola.

Front

What does it mean if a parabola opens upwards?

Back

If a parabola opens upwards, it has a minimum vertex, and the values of the function increase as you move away from the vertex.

Front

What does it mean if a parabola opens downwards?

Back

If a parabola opens downwards, it has a maximum vertex, and the values of the function decrease as you move away from the vertex.

Front

What is the standard form of a quadratic equation?

Back

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

Front

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

Back

You can determine this by looking at the coefficient 'a' in the quadratic equation. If 'a' is positive, the parabola opens upwards (minimum). If 'a' is negative, it opens downwards (maximum).

Front

What is the significance of the vertex in relation to the axis of symmetry?

Back

The vertex lies on the axis of symmetry, which means it is equidistant from the points on either side of the parabola.

Front

If the vertex of a parabola is at (3, 5), what is the equation of the axis of symmetry?

Back

The equation of the axis of symmetry is x = 3.

Front

What is the relationship between the roots of a quadratic equation and the axis of symmetry?

Back

The axis of symmetry is located exactly halfway between the two roots (x-intercepts) of the quadratic equation.