Vertex and Standard Form Flashcard

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 do you identify the vertex from the vertex form of a parabola?

Back

In the vertex form y = a(x - h)² + k, the vertex is the point (h, k).

Front

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

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is given by y = ax² + bx + c.

Front

How can you convert from standard form to vertex form?

Back

You can convert from standard form to vertex form by completing the square.

Front

What is the x-intercept of a parabola?

Back

The x-intercept is the point(s) where the graph of the parabola intersects the x-axis, found by setting y = 0.

Front

What is the significance of the vertex in a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on the direction it opens.

Front

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

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

What is the axis of symmetry in a parabola?

Back

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

Front

What is the relationship between the roots and the x-intercepts of a parabola?

Back

The roots of the quadratic equation are the x-values where the parabola intersects the x-axis, which are also the x-intercepts.