Transformations and Parent Functions

Front

What is a quadratic function?

Back

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

Front

What does it mean to reflect a function over the x-axis?

Back

Reflecting a function over the x-axis means to invert the output values, changing the sign of the function: if y = f(x), the reflected function is y = -f(x).

Front

How do you shift a function vertically?

Back

To shift a function vertically, you add or subtract a constant from the function: y = f(x) + k shifts it up by k units (if k > 0) or down by k units (if k < 0).

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is y = x², which is a parabola that opens upwards.

Front

How do you translate a function horizontally?

Back

To translate a function horizontally, you add or subtract a constant inside the function: y = f(x - h) shifts it right by h units (if h > 0) or left by h units (if h < 0).

Front

What is the absolute value function?

Back

The absolute value function is defined as y = |x|, which outputs the non-negative value of x.

Front

What is the effect of a negative sign in front of a quadratic function?

Back

A negative sign in front of a quadratic function, such as y = -x², reflects the graph over the x-axis, making it open downwards.

Front

What is the general form of a linear function?

Back

The general form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you identify a quadratic function from its graph?

Back

A quadratic function's graph is a parabola, which can open upwards or downwards and has a vertex as its highest or lowest point.

Front

What does it mean to shift a graph to the right?

Back

Shifting a graph to the right means to move every point of the graph horizontally to the right by a certain number of units.