Transformations of Quadratics

Front

What is the vertex of the quadratic equation y = -(x + 1)² + 4?

Back

(-1, 4)

Front

What happens to the graph of y = 4x² compared to y = x²?

Back

The graph becomes more narrow (stretches).

Front

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

Back

A Parabola.

Front

If the equation is y = (x - 3)², how does the graph move?

Back

The graph moves to the RIGHT 3 units.

Front

Describe the transformation of f(x) = x² into f(x) = (x - 5)² + 3.

Back

Opens up, shifts to the right 5, and shifts up 3.

Front

What is the standard form of a quadratic equation?

Back

y = ax² + bx + c.

Front

What does the 'a' value in the quadratic equation y = ax² + bx + c determine?

Back

The direction of the parabola (upward if a > 0, downward if a < 0).

Front

What is the axis of symmetry for the quadratic equation y = x² - 4x + 3?

Back

x = 2.

Front

How do you find the vertex of a quadratic in standard form?

Back

Use the formula x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

What effect does a negative 'a' value have on the graph of a quadratic function?

Back

It reflects the graph across the x-axis.