Unit 6 Flashcard 1

Front

What is the equation for the red function?

Back

g(x)=(x-1)^3

Front

What is the vertex of the function f(x)=(x-4)^2+3?

Back

(4,3)

Front

Describe the transformation of the graph y = -½(x + 4)^3 - 1.

Back

Reflected x-axis, Down 1, Left 4, Compression by a factor of 1/2

Front

Describe the transformation of the graph y = x^3 + 6.

Back

Up 6

Front

What is the general form of a cubic function?

Back

f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants.

Front

What does the vertex of a parabola represent?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

How do you find the vertex of a quadratic function in vertex form?

Back

For f(x) = a(x-h)^2 + k, the vertex is (h, k).

Front

What is the effect of a negative coefficient in front of a cubic function?

Back

It reflects the graph across the x-axis.

Front

What does a compression by a factor of 1/2 do to the graph of a function?

Back

It makes the graph 'wider' or less steep.

Front

What is the significance of the constant term in a polynomial function?

Back

It represents the y-intercept of the graph.