Transforming Quadratics Standard Form

Front

What does the 'a' value in a quadratic function determine?

Back

The 'a' value determines the width and direction of the parabola. A larger absolute value of 'a' makes the parabola narrower, while a smaller absolute value makes it wider.

Front

How does changing the 'c' value in the standard form quadratic equation (y=ax²+bx+c) affect the graph?

Back

Changing the 'c' value shifts the graph up or down without affecting its shape.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on the direction it opens.

Front

How can you identify the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) and then substituting x back into the function to find the y-coordinate.

Front

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

Back

A narrow quadratic function has a larger absolute value of 'a', which means it rises or falls more steeply.

Front

What is the effect of a negative 'a' value in a quadratic function?

Back

A negative 'a' value causes the parabola to open downwards.

Front

How do you determine if two quadratic functions have the same vertex?

Back

Two quadratic functions have the same vertex if their vertex coordinates (h, k) are identical.

Front

What is the significance of the 'b' value in a quadratic function?

Back

The 'b' value affects the position of the vertex and the axis of symmetry of the parabola.

Front

What happens to the graph of a quadratic function when 'a' is equal to 0?

Back

If 'a' is equal to 0, the function is no longer quadratic; it becomes a linear function.

Front

How can you compare two quadratic functions?

Back

You can compare their vertices, widths, and directions of opening by analyzing their 'a', 'b', and 'c' values.