Quadratics: Converting Between Forms

Front

What is the vertex form of a quadratic function?

Back

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

Front

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

Back

To convert from standard form f(x) = ax² + bx + c to vertex form, complete the square.

Front

What is the vertex of the parabola given by the equation y = 3(x + 5)² - 4?

Back

The vertex is (-5, -4).

Front

Convert the quadratic function f(x) = 3x² + 6x - 5 to vertex form.

Back

f(x) = 3(x + 1)² - 8.

Front

Convert the quadratic function f(x) = \frac{1}{2}x² - 8x + 3 to vertex form.

Back

f(x) = \frac{1}{2}(x - 8)² - 29.

Front

Convert the quadratic function f(x) = -x² + 10x - 4 to vertex form.

Back

f(x) = -(x - 5)² + 21.

Front

What is the factored form of the quadratic function f(x) = 4x² - 25?

Back

(2x - 5)(2x + 5).

Front

What does the 'a' value in the vertex form of a quadratic function 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 for the parabola given by the equation y = 3(x + 5)² - 4?

Back

The axis of symmetry is x = -5.

Front

How do you find the y-intercept of a quadratic function in standard form?

Back

The y-intercept can be found by evaluating f(0).