Transformations & Quadratics in Vertex Form Practice

Front

What transformation occurs when the coefficient of x^2 is greater than 1 in the quadratic function y = ax^2?

Back

The graph becomes narrower by a factor of a.

Front

What does a negative coefficient in front of x^2 indicate about the graph of a quadratic function?

Back

The graph opens downward.

Front

How does the addition of a constant outside the squared term in y = a(x-h)^2 + k affect the graph?

Back

It translates the graph vertically by k units.

Front

What effect does adding a constant inside the squared term (y = a(x-h)^2 + k) have on the graph?

Back

It translates the graph horizontally by h units.

Front

What is the vertex of the quadratic function in vertex form y = a(x-h)^2 + k?

Back

The vertex is the point (h, k).

Front

How does the value of 'a' in the vertex form y = a(x-h)^2 + k affect the width of the parabola?

Back

If |a| > 1, the parabola is narrower; if 0 < |a| < 1, it is wider.

Front

What is the effect of a vertical stretch on the graph of a quadratic function?

Back

It makes the graph steeper.

Front

How do you write the equation of a quadratic function that reflects across the x-axis and translates left and up?

Back

Use the form y = -a(x-h)^2 + k, where h is the horizontal shift and k is the vertical shift.

Front

What is the significance of the vertex in the context of a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola.

Front

How can you determine if a quadratic function is wider or narrower than the standard form y = x^2?

Back

Compare the coefficient of x^2; larger coefficients indicate a narrower graph.