Algebra 2 Review 1st Semest B

The domain of a quadratic function, written as $$f(x) = ax^2 + bx + c$$ , is all real numbers: @@(- ext{∞}, ext{∞})@@.

The range of a downward-opening quadratic function is from negative infinity to the y-coordinate of the vertex: $$(-\text{∞}, k]$$ , where $$k$$ is the maximum value.

The vertex of the function is the point (h, k).

The range of the absolute value function is $$[0, \text{∞})$$ .

A linear function has a constant rate of change.

The vertex can be found using the formula $$x = -\frac{b}{2a}$$ , and then substituting this value back into the equation to find the y-coordinate.

The standard form of a quadratic function is $$f(x) = ax^2 + bx + c$$ .

A function is increasing on an interval if, for any two points $$x_1$$ and $$x_2$$ in that interval, if $$x_1 < x_2$$ , then $$f(x_1) < f(x_2)$$ .

The domain is the set of all possible input values (x-values) for a function, while the range is the set of all possible output values (y-values).

Changing the value of 'a' affects the width and direction of the parabola: if $$a > 0$$ , it opens upwards; if $$a < 0$$ , it opens downwards.