Transforming Quadratic Function from Standard to Vertex Form

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is given by y = ax² + bx + c, where a, b, and c are constants.

Front

How do you convert a quadratic function from standard form to vertex form?

Back

To convert from standard form (y = ax² + bx + c) to vertex form (y = a(x-h)² + k), complete the square.

Front

What is vertex form of a quadratic function?

Back

The vertex form of a quadratic function is y = a(x-h)² + k, where (h, k) is the vertex of the parabola.

Front

What is the vertex of the function y = (x-1)² - 6?

Back

The vertex is (1, -6).

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 its width.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by x = h in vertex form.

Front

How do you find 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 y = ax² + bx + c.

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 equation y = x² - 4x + 3 into vertex form.

Back

y = (x-2)² - 1.

Front

What are the roots of the quadratic function?

Back

The roots (or x-intercepts) are the values of x where the function equals zero.