Quadratic Vertex Form

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is 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 indicates the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the vertex of the parabola in the equation y = ½(x - 4)² - 4?

Back

The vertex is the point (4, -4).

Front

What does it mean for a parabola to have a minimum?

Back

A parabola has a minimum when it opens upwards and the vertex is the lowest point on the graph.

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 of the parabola, dividing it into two mirror-image halves.

Front

How do you find the axis of symmetry from the vertex form?

Back

The axis of symmetry can be found using the formula x = h, where (h, k) is the vertex.

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 can you convert from standard form to vertex form?

Back

You can convert by completing the square.

Front

What are the roots of a quadratic equation?

Back

The roots are the x-values where the parabola intersects the x-axis, also known as x-intercepts.

Front

What is the significance of the green dashed line in a parabola?

Back

The green dashed line represents the axis of symmetry.