Vertex Form Quadratics

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 identify the vertex from the vertex form?

Back

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

Front

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

Back

The parameter 'a' indicates 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 quadratic function?

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 find the x-intercepts of a quadratic function in vertex form?

Back

To find the x-intercepts, set y = 0 and solve the equation 0 = a(x-h)² + k.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the value of 'a'.

Front

What is the maximum or minimum value of a quadratic function in vertex form?

Back

The maximum or minimum value is the y-coordinate of the vertex (k). It is a maximum if 'a' is negative and a minimum if 'a' is positive.

Front

How can you convert standard form to vertex form?

Back

You can convert standard form (y = ax² + bx + c) to vertex form by completing the square.

Front

What are the x-intercepts of the function y = 2(x-1)(x-3)?

Back

The x-intercepts are x = 1 and x = 3.

Front

What does it mean if a parabola has no real x-intercepts?

Back

If a parabola has no real x-intercepts, it means the vertex is above the x-axis (for a parabola opening upwards) or below the x-axis (for a parabola opening downwards) and does not cross the x-axis.