Exam 12/9

Front

What transformation changes the graph of f(x) = x² to g(x) = (x + 4)²?

Back

A horizontal translation 4 units to the left.

Front

Complete the square for the expression x² - 14x + ___.

Back

49.

Front

Solve for x: |x - 6| + 4 = 10.

Back

x = 12 and x = 0.

Front

Evaluate the piecewise function for f(-4).

Back

16.

Front

Complete the square: x² + 6x = 5.

Back

(x + 3)² = 14.

Front

What is the definition of a piecewise function?

Back

A function defined by multiple sub-functions, each applying to a certain interval of the domain.

Front

What does completing the square help to achieve in quadratic equations?

Back

It helps to rewrite the equation in vertex form, making it easier to analyze and graph.

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you find the vertex of a parabola given in standard form?

Back

Use the formula h = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

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

Back

The parabola opens upwards.