Quadratic Function In Vertex Form

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

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

Back

The parameter 'a' represents the vertical stretch or compression of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

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 y = a(x - h)² + k is the vertical line x = h.

Front

What is the vertex of the parabola given by the equation y = 3(x + 2)² - 5?

Back

The vertex of the parabola is (-2, -5).

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

A quadratic function opens upwards if the coefficient 'a' in the vertex form is positive, and it opens downwards if 'a' is negative.

Front

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

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

Front

Given the vertex form y = -2(x - 1)² + 3, what is the vertex?

Back

The vertex is (1, 3).

Front

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

Back

To convert from standard form (y = ax² + bx + c) to vertex form, you can complete the square.

Front

What is the effect of changing the value of 'h' in the vertex form of a quadratic function?

Back

Changing the value of 'h' shifts the graph of the parabola horizontally. If 'h' increases, the graph shifts to the right; if 'h' decreases, it shifts to the left.

Front

What is the effect of changing the value of 'k' in the vertex form of a quadratic function?

Back

Changing the value of 'k' shifts the graph of the parabola vertically. If 'k' increases, the graph shifts up; if 'k' decreases, it shifts down.