Quadratics and Transformations

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is f(x) = ax^2 + bx + c.

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x for which f(x) = 0, also known as the x-intercepts.

Front

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

Back

The vertex of a parabola in standard form f(x) = ax^2 + bx + c can be found using the formula x = -b/(2a) for the x-coordinate, and then substituting x back into the function to find the y-coordinate.

Front

What does the 'a' value in a quadratic function determine?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

Front

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

Back

Adding a constant to a quadratic function, f(x) = ax^2 + bx + c + k, results in a vertical translation of the graph by k units.

Front

What is the effect of changing the 'b' value in a quadratic function?

Back

Changing the 'b' value affects the position of the vertex and the axis of symmetry of the parabola.

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 = -b/(2a).

Front

What transformation occurs when you replace f(x) with f(x - h)?

Back

Replacing f(x) with f(x - h) results in a horizontal translation of the graph h units to the right.

Front

What transformation occurs when you replace f(x) with f(x) + k?

Back

Replacing f(x) with f(x) + k results in a vertical translation of the graph k units up.