Transformations of Quadratics

Front

What is a transformation of a quadratic function?

Back

A transformation of a quadratic function involves changing its position, shape, or orientation on the graph, typically through translations, reflections, stretches, or compressions.

Front

What does a reflection in the x-axis do to the graph of a quadratic function?

Back

A reflection in the x-axis flips the graph of the quadratic function over the x-axis, changing the sign of the coefficient of the x² term.

Front

What effect does a vertical stretch have on the graph of a quadratic function?

Back

A vertical stretch increases the distance between the points on the graph and the x-axis, making the parabola narrower.

Front

What does a vertical compression do to the graph of a quadratic function?

Back

A vertical compression decreases the distance between the points on the graph and the x-axis, making the parabola wider.

Front

How does a horizontal shift affect the graph of a quadratic function?

Back

A horizontal shift moves the graph left or right along the x-axis, depending on the sign of the value added or subtracted inside the parentheses.

Front

What is the effect of a vertical shift on the graph of a quadratic function?

Back

A vertical shift moves the graph up or down along the y-axis, depending on the value added or subtracted outside the parentheses.

Front

What does the coefficient of the x² term indicate about the parabola's direction?

Back

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

Front

What happens to the graph of y = 5(x - 5)² + 3 compared to y = x²?

Back

The graph narrows due to the vertical stretch by a factor of 5, shifts right by 5 units, and shifts up by 3 units.

Front

In the equation f(x) = 1/2(x + 9)² - 1, what transformations occur?

Back

The graph undergoes a vertical compression by a factor of 1/2, shifts left by 9 units, and shifts down by 1 unit.

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is f(x) = x², which is the simplest form of a quadratic function.