Review 1 Midterm Algebra II

The y-intercept is the point where the graph intersects the y-axis. For the function $$f(x) = -2(4^0) + 5 = 3$$ , the y-intercept is (0, 3).

To solve for m, first isolate $$m^2$$ : $$5m^2 = 130$$ , then $$m^2 = 26$$ . Taking the square root gives $$m = \pm \sqrt{26}$$ .

Using the distributive property: (7)(9) + (7)(-6i) + (2i)(9) + (2i)(-6i) = 63 - 42i + 18i - 12i^2 = 75 - 24i.

The vertex form of a parabola is $$y = a(x - h)^2 + k$$ , where (h, k) is the vertex. Here, the vertex is (4, -1).

The axis of symmetry is the vertical line that passes through the vertex. For this parabola, the axis of symmetry is $$x = 4$$ .

An exponential function is a mathematical function of the form $$f(x) = a \times b^x$$ , where $$a$$ is a constant, $$b$$ is a positive real number, and @@b eq 1@@.

The general form of a quadratic equation is $$ax^2 + bx + c = 0$$ , where $$a$$ , $$b$$ , and $$c$$ are constants and @@a eq 0@@.

The roots can be found using the formula $$x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$$ .

The discriminant, given by $$b^2 - 4ac$$ , indicates the nature of the roots: if positive, two distinct real roots; if zero, one real root; if negative, two complex roots.

A rational number can be expressed as a fraction $$\frac{p}{q}$$ where $$p$$ and $$q$$ are integers and $$q \neq 0$$ . An irrational number cannot be expressed as such a fraction.