Standard to Vertex Form

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you convert from standard form to vertex form?

Back

To convert from standard form to vertex form, complete the square on the quadratic expression.

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola represents the highest or lowest point of the graph, depending on whether it opens upwards or downwards.

Front

What is the significance of the 'a' value in the vertex form?

Back

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

Front

Convert f(x) = 2x² + 8x + 3 to vertex form.

Back

f(x) = 2(x + 2)² - 5.

Front

Convert f(x) = -x² + 4x - 1 to vertex form.

Back

f(x) = -(x - 2)² + 3.

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, given by the equation x = h.

Front

How do you find the vertex from the standard form?

Back

The vertex can be found using the formula h = -b/(2a) and k = f(h).

Front

What is the effect of changing the 'h' value in the vertex form?

Back

Changing the 'h' value shifts the graph horizontally; if h is positive, the graph shifts left, and if h is negative, it shifts right.