Standard to Vertex Form

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation 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 is the vertex of the parabola given by f(x) = (x - 3)² + 2?

Back

The vertex of the parabola is (3, 2).

Front

What does the 'a' value in vertex form indicate about the parabola?

Back

The 'a' value indicates 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 the equation f(x) = x² - 4x + 3 into vertex form.

Back

f(x) = (x - 2)² - 1.

Front

What is the axis of symmetry for the parabola given by f(x) = (x + 5)² - 10?

Back

The axis of symmetry is x = -5.

Front

How do you find the vertex from the standard form f(x) = ax² + bx + c?

Back

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

Front

Convert the equation y = 2x² + 8x + 6 into vertex form.

Back

y = 2(x + 2)² - 2.

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.