Writing Quadratics in 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

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

Back

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

Front

What does the 'a' in the vertex form of a quadratic equation represent?

Back

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

Front

What is the axis of symmetry in a parabola?

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 convert standard form to vertex form?

Back

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

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 whether it opens upwards or downwards.

Front

If a quadratic equation is in vertex form, how can you determine if it opens upwards or downwards?

Back

If 'a' is greater than 0, the parabola opens upwards; if 'a' is less than 0, it opens downwards.

Front

What is the formula to find the vertex from standard form?

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h), where f(x) is the original quadratic function.

Front

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

Back

The axis of symmetry always passes through the vertex of the parabola.

Front

How do you identify the vertex from the equation y = 3(x + 5)² - 4?

Back

The vertex is (-5, -4).