Standard to Vertex Form for Quadratics

Front

What is the standard form of a quadratic equation?

Back

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

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = 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 represented by the equation y = (x + 3)² - 11?

Back

The vertex of the parabola is (-3, -11).

Front

What does the 'a' value in the 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

What is the axis of symmetry for the parabola y = (x - 5)² - 15?

Back

The axis of symmetry is the vertical line x = 5.

Front

How do you find the y-intercept of a quadratic equation in vertex form?

Back

To find the y-intercept, set x = 0 in the vertex form equation and solve for y.

Front

What is the y-intercept of the equation y = (x + 8)² + 36?

Back

The y-intercept is (0, 100).

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

What is the formula for finding the vertex (h, k) from the standard form y = ax² + bx + c?

Back

The vertex can be found using h = -b/(2a) and k = f(h), where f(h) is the value of the function at x = h.