Shifting Parabolas

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola.

Front

What do we call the graph of a quadratic function?

Back

A parabola.

Front

If f(x) = x², what is the equation of the graph shifted 3 units to the right?

Back

g(x) = (x - 3)².

Front

What is the equation of a parabola that opens upwards and is shifted 5 units up from y = x²?

Back

y = x² + 5.

Front

What transformation maps f(x) = x² to g(x) = (x + 4)²?

Back

A translation shifting f(x) 4 units to the left.

Front

What is the vertex of the parabola given by the equation y = (x - 2)² + 3?

Back

The vertex is (2, 3).

Front

How does the graph of y = x² compare to y = -x²?

Back

y = x² opens upwards, while y = -x² opens downwards.

Front

What effect does the coefficient 'a' have in the equation y = a(x - h)² + k?

Back

The coefficient 'a' determines the width and direction of the parabola (narrower if |a| > 1, wider if |a| < 1, and opens upwards if a > 0, downwards if a < 0).

Front

What is the standard form of a quadratic function?

Back

y = ax² + bx + c.

Front

What is the significance of the 'h' and 'k' in the vertex form of a parabola y = a(x - h)² + k?

Back

The 'h' represents the x-coordinate of the vertex, and 'k' represents the y-coordinate of the vertex.