Transformations of Parabolas

Front

What transformation happens in the equation: y = (x - 5)² - 3?

Back

The graph is shifted to the right 5 units and down 3 units.

Front

What is the shape of the graph of y = x²?

Back

A Parabola.

Tags

CCSS.HSF-IF.C.7A

Front

Which equation best fits the transformed function shown in red?

Back

f(x) = (x - 3)² - 1.

Front

What is the most basic equation of a parabola, also known as the parent function?

Back

y = x².

Front

Which way does the graph move in the equation y = (x + 4)²?

Back

Graph moves to the LEFT 4 units.

Tags

CCSS.HSF-IF.C.7A

Front

What is a parabola?

Back

A parabola is a U-shaped graph that represents a quadratic function.

Tags

CCSS.HSF-IF.C.7A

Front

What does the vertex of a parabola represent?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

How does the coefficient of x² affect the direction of a parabola?

Back

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

Tags

CCSS.HSF-IF.C.7A

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves.

Front

What is the effect of adding a constant to the equation of a parabola?

Back

Adding a constant shifts the graph vertically.