Vertex Form of a Quadratic Function

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you find the vertex from the vertex form?

Back

The vertex (h, k) can be directly read from the vertex form y = a(x - h)² + k.

Front

What does the 'a' in the vertex form indicate?

Back

The 'a' value determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.

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, given by the equation x = h.

Front

How do you determine the axis of symmetry from the vertex form?

Back

The axis of symmetry can be found using the formula x = h, where (h, k) is the vertex.

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 whether it opens upwards or downwards.

Front

What are the roots of a quadratic function?

Back

The roots (or zeros) are the x-values where the quadratic function intersects the x-axis, found by solving the equation y = 0.

Front

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

Back

The maximum or minimum value occurs at the vertex (h, k) of the parabola. If 'a' is positive, k is the minimum; if negative, k is the maximum.

Front

What is the relationship between the vertex and the graph of a parabola?

Back

The vertex is the point where the parabola changes direction and is the highest or lowest point on the graph.

Front

How do you convert standard form to vertex form?

Back

To convert from standard form y = ax² + bx + c to vertex form, complete the square.