Transformations of Quadratics

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What effect does changing the coefficient 'a' in f(x) = ax² have on the graph?

Back

Changing 'a' affects the width and direction of the parabola. If |a| > 1, the graph is narrower; if 0 < |a| < 1, it is wider. If 'a' is negative, the parabola opens downwards.

Front

What is the vertex of a parabola?

Back

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

Front

How do you find the vertex of the parabola given in vertex form y = a(x-h)² + k?

Back

The vertex is the point (h, k).

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 for the vertex form.

Front

What does it mean for a parabola to have a maximum value?

Back

A parabola has a maximum value if it opens downwards (a < 0), and the maximum value occurs at the vertex.

Front

What does it mean for a parabola to have a minimum value?

Back

A parabola has a minimum value if it opens upwards (a > 0), and the minimum value occurs at the vertex.

Front

How does the graph of g(x) = 5x² compare to f(x) = x²?

Back

The graph of g(x) is narrower than the graph of f(x) because the coefficient 5 is greater than 1.

Front

What is the effect of adding a constant 'k' to the function f(x) = x²?

Back

Adding a constant 'k' shifts the graph vertically. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What is the effect of changing the value of 'h' in the function f(x) = (x-h)²?

Back

Changing 'h' shifts the graph horizontally. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.