Graphing Quadratics in Vertex Form

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 about the parabola?

Back

The 'a' value determines 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 axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = h, where (h, k) is the vertex.

Front

How do you find the vertex of a parabola given in vertex form?

Back

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

Front

What is the maximum or minimum value of a parabola?

Back

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

Front

What is the significance of the vertex in graphing quadratics?

Back

The vertex is the highest or lowest point of the parabola and serves as a key reference point for graphing.

Front

How can you determine if a parabola opens upwards or downwards?

Back

You can determine the direction by looking at the 'a' value in the vertex form. If 'a' > 0, it opens upwards; if 'a' < 0, 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 do you convert from standard form to vertex form?

Back

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

Front

What is the formula for finding the x-coordinate of the vertex from standard form?

Back

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