Vertex Form, Standard Form, Factored Form

Front

What is the axis of symmetry for a quadratic function?

Back

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 from vertex form to standard form?

Back

To convert from vertex form f(x) = a(x - h)^2 + k to standard form f(x) = ax^2 + bx + c, expand the equation and simplify.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the function crosses the x-axis, found by setting f(x) = 0 and solving for x.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the factored form of a quadratic function?

Back

The factored form of a quadratic function is f(x) = a(x - r_1)(x - r_2), where r_1 and r_2 are the roots (x-intercepts) of the function.

Front

How do you find the vertex of a quadratic function in standard form?

Back

Front

What is the significance of the 'a' value in 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

How do you determine the direction of a parabola?

Back

The direction of a parabola is determined by the sign of the 'a' coefficient in the quadratic function: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the relationship between the roots and the x-intercepts of a quadratic function?

Back

The roots of a quadratic function are the values of x that make the function equal to zero, which correspond to the x-intercepts on the graph.