Axis of Symmetry and Vertex

Front

What is the axis of symmetry for the quadratic function y = ax^2 + bx + c?

Back

The axis of symmetry is given by the formula x = -b/(2a).

Front

How do you find the vertex of a parabola given in standard form?

Back

The vertex can be found using the formula (h, k) where h = -b/(2a) and k = f(h).

Front

What does the letter 'a' represent in the quadratic equation y = ax^2 + bx + c?

Back

The letter 'a' determines the direction in which the parabola opens: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c.

Front

How can you determine if a parabola opens upwards or downwards?

Back

By examining the coefficient 'a' in the quadratic equation: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the vertex of the parabola represented by the equation y = 3x^2 - 6x + 4?

Back

The vertex is (1, -1).

Front

What is the axis of symmetry for the quadratic function y = 2x^2 + 4x + 1?

Back

The axis of symmetry is x = -1.

Front

How do you convert the quadratic equation from standard form to vertex form?

Back

You can convert it by completing the square to express it as y = a(x - h)^2 + k.

Front

What is the significance of the vertex in a parabola?

Back

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

Front

What is the formula to find the y-coordinate of the vertex?

Back

The y-coordinate of the vertex can be found by substituting h into the original equation: k = f(h).