Quadratic Functions-Vertex and Standard Form

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, represented as (h, k) in the vertex form of a quadratic function.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = h, where (h, k) is the vertex.

Front

What is the standard form of a quadratic function?

Back

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

Front

What is the vertex form of a quadratic function?

Back

The vertex form is written as f(x) = a(x - h)^2 + k, where (h, k) is the vertex.

Front

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

Back

To find the vertex from standard form, use the formula h = -b/(2a) and then substitute h back into the function to find k.

Front

What does the 'a' value in a quadratic function indicate?

Back

The 'a' value determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the significance of the 'k' value in vertex form?

Back

The 'k' value represents the y-coordinate of the vertex and indicates the vertical shift of the parabola.

Front

How can you determine if a quadratic function has a maximum or minimum value?

Back

If 'a' is positive, the function has a minimum value at the vertex; if 'a' is negative, it has a maximum value.

Front

What is the formula to find the axis of symmetry from the vertex form?

Back

The axis of symmetry is given by the equation x = h, where (h, k) is the vertex.

Front

Find the vertex of f(x) = 2x^2 + 8x + 6.

Back

The vertex is (-2, -2).