standard, vertex, and factored form

Front

What are the x-intercepts of a quadratic function in factored form?

Back

The x-intercepts are the values of x that make the function equal to zero. For a function in factored form, y = a(x - r1)(x - r2), the x-intercepts are r1 and r2.

Front

How do you convert a quadratic function from standard form to vertex form?

Back

To convert from standard form (f(x) = ax^2 + bx + c) to vertex form (f(x) = a(x - h)^2 + k), you can complete the square.

Front

What is the vertex of a parabola in vertex form?

Back

In vertex form, f(x) = a(x - h)^2 + k, the vertex is the point (h, k).

Front

What does it mean for a parabola to open up or down?

Back

A parabola opens up if the coefficient 'a' in the vertex form is positive, and it opens down if 'a' is negative.

Front

How can you identify the vertex of a parabola given in standard form?

Back

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

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 whether it opens up or down.

Front

What is the factored form of a quadratic function?

Back

The factored form of a quadratic function is expressed as y = a(x - r1)(x - r2), where r1 and r2 are the roots or x-intercepts.

Front

How do you find the y-intercept of a quadratic function?

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the point (0, f(0)).

Front

What is the relationship between the roots and the vertex of a parabola?

Back

The roots (x-intercepts) and the vertex are related; the vertex lies on the axis of symmetry, which is halfway between the roots.

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.