Algebra 1 9.1 Graphing f(x)=ax^2

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What does the coefficient 'a' in the quadratic function f(x) = ax^2 represent?

Back

The coefficient 'a' determines the direction and the width of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is a vertical stretch in the context of quadratic functions?

Back

A vertical stretch occurs when the absolute value of 'a' is greater than 1, making the parabola narrower.

Front

What is a vertical shrink in the context of quadratic functions?

Back

A vertical shrink occurs when the absolute value of 'a' is less than 1, making the parabola wider.

Front

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

Back

A negative 'a' reflects the graph over the x-axis.

Front

How does the graph of f(x) = x^2 compare to g(x) = 4x^2?

Back

The graph of g(x) = 4x^2 is a vertical stretch of the graph of f(x) = x^2 by a factor of 4.

Front

How does the graph of f(x) = x^2 compare to g(x) = 1.5x^2?

Back

The graph of g(x) = 1.5x^2 is a vertical stretch of the graph of f(x) = x^2 by a factor of 1.5.

Front

What does it mean for a graph to have a vertical shrink factor of 1/3?

Back

It means the graph is wider than the standard parabola f(x) = x^2, as the coefficient 'a' is less than 1.

Front

What is the effect of a vertical translation of a quadratic function?

Back

A vertical translation shifts the graph up or down without changing its shape.

Front

How does the graph of f(x) = -5x^2 compare to g(x) = 5x^2?

Back

The graph of g(x) = 5x^2 is reflected over the x-axis to form f(x) = -5x^2.