Vertex Form of 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 does the value of 'a' in the vertex form affect the graph of the quadratic?

Back

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

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola represents the turning point of the graph, which is the maximum or minimum point depending on the direction the parabola opens.

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 effect of translating a quadratic function to the left or right?

Back

Translating a quadratic function to the left or right involves changing the 'h' value in the vertex form. For example, y = a(x - h)² + k translates the graph h units to the right if h is positive and h units to the left if h is negative.

Front

What is the significance of the 'k' value in the vertex form?

Back

The 'k' value in the vertex form y = a(x - h)² + k represents the vertical translation of the parabola. It shifts the graph up if k is positive and down if k is negative.

Front

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

Back

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

Front

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

Back

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

Front

What is the axis of symmetry in the vertex form of a quadratic equation?

Back

In the vertex form y = a(x - h)² + k, the axis of symmetry is the line x = h.

Front

How do you determine the direction in which a parabola opens?

Back

The direction in which a parabola opens is determined by the sign of 'a' in the vertex form. If 'a' is positive, it opens upwards; if 'a' is negative, it opens downwards.