Converting Standard to Vertex Form of Quadratics

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?

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?

Back

The 'a' value indicates the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

Front

Convert the standard form y = 3x² + 6x + 1 to vertex form.

Back

y = 3(x + 1)² - 2.

Front

What is the process to convert from standard form to vertex form?

Back

1. Complete the square on the quadratic expression. 2. Factor out the coefficient of x² if necessary. 3. Rewrite the equation in vertex form.

Front

Convert the standard form y = x² - 4x + 7 to vertex form.

Back

y = (x - 2)² + 3.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

Convert the standard form y = -2x² + 8x - 5 to vertex form.

Back

y = -2(x - 2)² + 3.

Front

What is the axis of symmetry in a quadratic function?

Back

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

Front

Convert the standard form y = 4x² - 16x + 15 to vertex form.

Back

y = 4(x - 2)² - 1.