Mid-Term Study Guide A2

Front

What is the translation of the parent function f(x) = |x| to obtain g(x) = 2 + |x + 3|?

Back

Left 3 units and up 2 units.

Front

What is the vertex form of a parabola with vertex (-1, 8) that passes through (1, 0)?

Back

y = -2(x + 1)² + 8.

Front

Simplify the expression (m+n)(m²−2mn+2n²).

Back

m³ - m²n + 2n³.

Front

Simplify the expression (−6x³ − 4x² − 8) + (x³ − x² − 9x + 4).

Back

-5x³ + 5x² - 9x - 4.

Front

What is the range of a graphed function that includes the values from -4 to 2, not including 2?

Back

[-4, 2).

Front

Define the vertex of a parabola.

Back

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

Front

What does the term 'parent function' refer to in mathematics?

Back

A parent function is the simplest form of a function in a family of functions.

Front

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

Back

The vertex can be found using the formula x = -b/(2a) from the quadratic equation ax² + bx + c.

Front

What is the significance of the 'a' value in the vertex form of a parabola?

Back

The 'a' value determines the direction and width of the parabola; if 'a' is positive, it opens upwards, and if negative, it opens downwards.

Front

What is the effect of translating a function vertically?

Back

Translating a function vertically shifts the graph up or down without changing its shape.