Vertex Form Quadratics

Front

What is the vertex form of a quadratic equation?

Back

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

Front

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

Back

The 'a' value determines the direction of the parabola's opening: if 'a' is positive, it opens upwards; if 'a' is 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 divides the parabola into two mirror-image halves, given by the equation x = h in the vertex form.

Front

How do you find the vertex from the vertex form?

Back

The vertex can be found directly from the vertex form f(x) = a(x-h)² + k as the point (h, k).

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the quadratic function crosses the x-axis, found by setting f(x) = 0.

Front

How can you determine the direction a parabola opens?

Back

The direction of the parabola can be determined by the sign of 'a': positive 'a' opens upwards, negative 'a' opens downwards.

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 convert standard form to vertex form?

Back

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

Front

What is the formula for finding the axis of symmetry from standard form?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the standard form ax² + bx + c.

Front

What is the effect of changing the 'k' value in the vertex form?

Back

Changing the 'k' value shifts the parabola vertically: increasing 'k' moves it up, while decreasing 'k' moves it down.