Transformations of Quadratics

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is f(x) = x².

Front

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

Back

A negative coefficient reflects the graph across the x-axis.

Front

How does the value of 'a' in the equation y = a(x - h)² + k affect the graph?

Back

The value of 'a' affects the width and direction of the parabola. If |a| > 1, the graph is narrower; if 0 < |a| < 1, it is wider.

Front

What does the vertex form of a quadratic equation look like?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex.

Front

What transformation does g(x) = (x + 3)² represent compared to f(x) = x²?

Back

It represents a horizontal shift to the left by 3 units.

Front

What transformation does g(x) = x² - 5 represent compared to f(x) = x²?

Back

It represents a vertical shift downward by 5 units.

Front

What does it mean for a quadratic function to be 'narrower'?

Back

A quadratic function is 'narrower' when the absolute value of 'a' is greater than 1.

Front

What does it mean for a quadratic function to be 'wider'?

Back

A quadratic function is 'wider' when the absolute value of 'a' is less than 1.

Front

If g(x) = -2x², what transformations have occurred compared to f(x) = x²?

Back

The graph is reflected across the x-axis and is narrower.

Front

What is the effect of adding a constant to a quadratic function, such as in g(x) = x² + 3?

Back

It results in a vertical shift upward by 3 units.