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

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, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, and it passes through the vertex.

Front

How do you find the vertex from the vertex form of a quadratic equation?

Back

The vertex can be found directly from the vertex form y = a(x - h)² + k as the point (h, 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 whether it opens upwards or downwards.

Front

What are the x-intercepts of a parabola?

Back

The x-intercepts are the points where the parabola crosses the x-axis, found by setting y = 0 and solving for x.

Front

How can you determine if a parabola has a maximum or minimum value?

Back

If 'a' in the vertex form is negative, the parabola has a maximum value; if 'a' is positive, it has a minimum value.

Front

What is the relationship between the vertex and the axis of symmetry?

Back

The axis of symmetry always passes through the vertex of the parabola.

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.

Front

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

Back

Changing the 'h' value shifts the parabola left or right along the x-axis.