Cumulative Review-1st Semester Algebra 2

Front

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

Back

The graph is transformed 3 units left, 2 units up, and reflected across the x-axis.

Front

Describe the transformations of the function f(x) = -2|x + 3| - 1.

Back

The graph is transformed left 3 units, vertically stretched by a factor of 2, reflected over the x-axis, and shifted down 1 unit.

Front

Solve the inequality: 2x^2 + 5x ≥ 12.

Back

The solution is (−∞, -4] U [1.5, ∞).

Front

Factor the expression: 2m^2 + 3m - 9.

Back

The factored form is (m + 3)(2m - 3).

Front

Complete the square for the expression: x^2 + 14x + ____.

Back

The completed square is x^2 + 14x + 49.

Front

What does it mean to complete the square in a quadratic expression?

Back

Completing the square involves rewriting a quadratic in the form (x + p)^2 + q, making it easier to solve or graph.

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

How do you find 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 ax^2 + bx + c.

Front

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

Back

A negative coefficient reflects the graph across the x-axis.

Front

What is a vertical stretch in the context of transformations?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.