Transformations of Quadratics

Front

What is the parent function of a quadratic equation?

Back

f(x) = x²

Front

What transformation does the equation f(x) = (x - 2)² represent?

Back

Horizontal shift right 2 units

Front

What transformation does the equation f(x) = (x + 3)² represent?

Back

Horizontal shift left 3 units

Front

What transformation does the equation f(x) = x² + 5 represent?

Back

Vertical shift up 5 units

Front

What transformation does the equation f(x) = x² - 4 represent?

Back

Vertical shift down 4 units

Front

What does a vertical stretch by a factor of 3 do to the function f(x) = x²?

Back

It transforms to g(x) = 3x².

Front

What does a vertical shrink by a factor of 1/2 do to the function f(x) = x²?

Back

It transforms to g(x) = 1/2x².

Front

What is the axis of symmetry for the parabola represented by the equation f(x) = (x - 1)² + 2?

Back

x = 1

Front

How does the equation g(x) = -x² transform the parent function f(x) = x²?

Back

It reflects the parabola over the x-axis.

Front

What transformation does the equation f(x) = 2(x - 1)² + 3 represent?

Back

Vertical stretch by a factor of 2, horizontal shift right 1 unit, vertical shift up 3 units.