Vertex Form -- Quadratics

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation 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 of a parabola given in vertex form?

Back

To find the vertex of a parabola in vertex form y = a(x - h)² + k, the vertex is the point (h, k).

Front

What does the 'a' value in the vertex form of a quadratic equation indicate?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c.

Front

How can you convert a quadratic equation from standard form to vertex form?

Back

To convert from standard form to vertex form, you can complete the square.

Front

What is the axis of symmetry for a parabola given in vertex form?

Back

The axis of symmetry for a parabola in vertex form y = a(x - h)² + k is the vertical line x = h.

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 direction it opens.

Front

How do you determine if a quadratic function opens upwards or downwards?

Back

If the 'a' value in the vertex form y = a(x - h)² + k is positive, the parabola opens upwards; if negative, it opens downwards.

Front

What is the formula to find the vertex of a quadratic function given in standard form?

Back

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

Front

What is the relationship between the vertex and the roots of a quadratic function?

Back

The vertex is the midpoint of the roots of the quadratic function, and it lies on the axis of symmetry.