Quadratic Transformations Mixed

Front

In the vertex form f(x) = a(x - h)² + k, what does the 'a' value do?

Back

The 'a' value determines the vertical stretch or compression of the parabola. If |a| > 1, the parabola is narrower; if 0 < |a| < 1, it is wider.

Front

What effect does changing the 'h' value have in the vertex form f(x) = a(x - h)² + k?

Back

The 'h' value shifts the graph of the function left or right. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.

Front

What does the 'k' value represent in the vertex form f(x) = a(x - h)² + k?

Back

The 'k' value shifts the graph of the function up or down. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

Which function represents a translation of 2 units right and a vertical stretch by a factor of 5?

Back

f(x) = 5(x - 2)².

Front

How does a negative 'a' value affect the graph of a quadratic function?

Back

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

Front

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

Back

A vertical stretch makes the parabola narrower, while a vertical compression makes it wider.

Front

If f(x) = x², what is the rule for g(x) if g is a translation 7 units right and a reflection in the x-axis?

Back

g(x) = -(x - 7)².

Front

Which quadratic function is the narrowest among the following: f(x)=1/2x², f(x)=x², f(x)=3x², f(x)=5x²?

Back

f(x)=5x² is the narrowest.

Front

What is the vertex form of a quadratic function?

Back

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

Front

What does the term 'translation' mean in the context of quadratic functions?

Back

Translation refers to shifting the graph of the function horizontally or vertically without changing its shape.