Transformations of Quadratic Functions

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is y = x².

Front

How does the coefficient of x² affect the width of a parabola?

Back

If the coefficient is greater than 1, the parabola is narrower than the parent function. If it is between 0 and 1, the parabola is wider.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

What are transformations in the context of quadratic functions?

Back

Transformations include translations, reflections, and rotations that change the position or orientation of the graph.

Front

How do you find the vertex of the function y = a(x - h)² + k?

Back

The vertex is at the point (h, k).

Front

What does a negative coefficient in front of x² indicate about the parabola?

Back

A negative coefficient indicates that the parabola opens downward.

Front

What is the effect of adding a constant outside the squared term in a quadratic function?

Back

Adding a constant outside the squared term translates the graph vertically.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that passes through the vertex, given by the equation x = h.

Front

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

Back

If the coefficient of x² is positive, it opens upwards; if negative, it opens downwards.

Front

What is the standard form of a quadratic function?

Back

The standard form is y = ax² + bx + c.