What is the y-intercept of the function $$f(x) = -2(4^x) + 5$$ ?

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).

How do you solve the equation $$5m^2 - 3 = 127$$ by square roots?

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

What is the vertex of the parabola represented by $$y = -(x - 4)^2 - 1$$ ?

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).

What is the axis of symmetry for the parabola $$y = -(x - 4)^2 - 1$$ ?

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

How do you find the roots of a quadratic equation using the quadratic formula?

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

What does the discriminant of a quadratic equation tell you?

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.

What is the difference between a rational and an irrational number?

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.

Define a complex number.

A complex number is a number of the form $$a + bi$$ , where $$a$$ and $$b$$ are real numbers, and $$i$$ is the imaginary unit, defined as $$i^2 = -1$$ .

What is the standard form of a linear equation?

The standard form of a linear equation is $$Ax + By = C$$ , where $$A$$ , $$B$$ , and $$C$$ are integers, and $$A$$ and $$B$$ are not both zero.

How do you perform polynomial long division?

To perform polynomial long division, divide the leading term of the dividend by the leading term of the divisor, multiply the entire divisor by this result, subtract from the dividend, and repeat with the new polynomial.

What is the significance of the leading coefficient in a polynomial?

The leading coefficient determines the end behavior of the polynomial function. If it is positive, the graph rises to the right; if negative, it falls to the right.

What is a function's domain?

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Review 1 Midterm Algebra II Flashcard

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15 questions

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1.

FLASHCARD QUESTION

Front

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2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

Simplify the expression (7 + 2i)(9 - 6i).

Back

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

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Define an exponential function.

Back

7.

FLASHCARD QUESTION

Front

What is the general form of a quadratic equation?

Back

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