Vertex Form Quadratics

Front

What is the vertex of a quadratic function in vertex form?

Back

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

Front

How do you find the axis of symmetry for a quadratic function in vertex form?

Back

The axis of symmetry for a quadratic function in vertex form, f(x) = a(x-h)² + k, is the vertical line x = h.

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

How can you convert from vertex form to standard form?

Back

To convert from vertex form f(x) = a(x-h)² + k to standard form, expand the equation: f(x) = a(x² - 2hx + h²) + k.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts of a quadratic function are the points where the graph intersects the x-axis, found by solving f(x) = 0.

Front

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

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What does the 'h' value represent in the vertex form of a quadratic function?

Back

The 'h' value represents the x-coordinate of the vertex of the parabola.

Front

What does the 'k' value represent in the vertex form of a quadratic function?

Back

The 'k' value represents the y-coordinate of the vertex of the parabola.

Front

How do you determine the vertex from the standard form of a quadratic function?

Back

To find the vertex from standard form f(x) = ax² + bx + c, use the formula: vertex x = -b/(2a) and substitute back to find y.

Front

What is the relationship between the vertex and the axis of symmetry?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola.