Quadratic Transformations

Front

What is the vertex form of a quadratic function?

Back

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

Front

What does the 'h' value represent in the vertex form?

Back

The 'h' value represents the horizontal shift of the parabola. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.

Front

What does the 'a' value indicate in the vertex form?

Back

The 'a' value indicates the direction and width of the parabola. If a is positive, the parabola opens upwards; if a is negative, it opens downwards. The larger the absolute value of a, the narrower the parabola.

Front

What effect does changing the 'k' value have on the graph of a quadratic function?

Back

Changing the 'k' value shifts the graph vertically. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

How do you find the vertex of a parabola given in standard form?

Back

To find the vertex of a parabola in standard form y = ax² + bx + c, use the formula h = -b/(2a) and k = f(h).

Front

What is the effect of adding a constant to a quadratic function?

Back

Adding a constant to a quadratic function shifts the graph vertically. For example, f(x) = x² + 3 shifts the graph up by 3 units.

Front

What is the equation of a parabola that opens downwards and has a vertex at (2, -3)?

Back

The equation is f(x) = -a(x - 2)² - 3, where 'a' is a positive constant that determines the width.

Front

If a parabola is represented by f(x) = (x - 4)², what is its vertex?

Back

The vertex of the parabola is (4, 0).

Front

What does it mean for a parabola to be 'reflected over the x-axis'?

Back

A parabola is reflected over the x-axis when the 'a' value in the vertex form is negative, causing the parabola to open downwards.

Front

How do you determine the direction a parabola opens based on its equation?

Back

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