Quadratic Transformations Review

Front

What does the coefficient in front of the squared term in a quadratic equation indicate?

Back

It indicates the vertical stretch or shrink of the parabola. A value greater than 1 indicates a vertical stretch, while a value between 0 and 1 indicates a vertical shrink.

Front

What is the effect of adding a constant to the end of a quadratic equation?

Back

It translates the graph vertically. If the constant is positive, the graph shifts up; if negative, it shifts down.

Front

What does the term (x - h) in the equation y = a(x - h)^2 + k represent?

Back

It represents a horizontal translation of the graph. The graph shifts to the right by h units if h is positive and to the left if h is negative.

Front

In the equation y = a(x - h)^2 + k, what does 'k' represent?

Back

'k' represents the vertical translation of the graph. It shifts the graph up if k is positive and down if k is negative.

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is y = x^2.

Front

How does a negative coefficient affect the graph of a quadratic function?

Back

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

Front

What is the vertex form of a quadratic equation?

Back

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

Front

What does it mean if a quadratic function has a vertex at (h, k)?

Back

It means that the point (h, k) is the highest or lowest point of the parabola, depending on the direction it opens.

Front

What is the effect of a vertical stretch by a factor of 'a' in the equation y = ax^2?

Back

It makes the parabola narrower if |a| > 1 and wider if 0 < |a| < 1.

Front

How do you determine the direction in which a parabola opens?

Back

If the coefficient 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.