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 f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

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

Back

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

Front

What does the parameter 'a' in the vertex form indicate about the parabola?

Back

The parameter 'a' indicates the direction of the parabola (upward if a > 0, downward if a < 0) and its width (larger |a| means a narrower parabola).

Front

How can you find the y-intercept of a quadratic function in vertex form?

Back

To find the y-intercept, substitute x = 0 into the vertex form equation and solve for f(0).

Front

What is the significance of the vertex in the graph of 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 a quadratic equation from standard form to vertex form?

Back

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

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that passes through the vertex, given by the equation x = h.

Front

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

Back

The direction of the parabola is determined by the sign of the coefficient 'a' in the vertex form: if a > 0, it opens upward; if a < 0, it opens downward.

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 ax² + bx + c.

Front

What is the relationship between the vertex and the y-intercept in a quadratic function?

Back

The vertex and y-intercept are both points on the graph of the quadratic function, but they represent different characteristics: the vertex is the maximum or minimum point, while the y-intercept is where the graph crosses the y-axis.