Quadratic Function 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

How can you determine if a parabola opens upwards or downwards?

Back

A parabola opens upwards if the coefficient 'a' in the vertex form y = a(x - h)² + k 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 represents the highest or lowest point of the parabola, depending on whether it opens downwards or upwards.

Front

What does the axis of symmetry represent in a parabola?

Back

The axis of symmetry is a vertical line that passes through the vertex, dividing the parabola into two mirror-image halves.

Front

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

Back

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

Front

What transformation does the equation y = (x - 3)² represent?

Back

It represents a horizontal shift of the graph 3 units to the right.

Front

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

Back

Changing 'a' affects the width and direction of the parabola; larger absolute values of 'a' make the parabola narrower, while smaller values make it wider.

Front

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

Back

To find the y-intercept, set x = 0 in the vertex form equation and solve for y.

Front

What is the maximum or minimum value of a quadratic function in vertex form?

Back

The maximum or minimum value is the y-coordinate of the vertex (k) in the vertex form y = a(x - h)² + k.

Front

How do you identify the direction of a parabola from its equation?

Back

If the coefficient 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.