Quadratic Functions
This form of a quadratic function is written as f(x) = ax² + bx + c, where a ≠ 0.
What is standard form?
This test uses the leading term of a polynomial to determine what happens to the function's values as x approaches positive or negative infinity.
What is the Leading Coefficient Test?
This division method is especially efficient when dividing a polynomial by a linear factor of the form (x - k).
What is synthetic division?
The square root of -1 is represented by this letter in complex numbers.
What is i?
A vertical line that a rational function approaches but never touches as x approaches a certain value.
What is a vertical asymptote?
This is the name for the point where a parabola reaches its maximum or minimum value.
What is the vertex?
A polynomial function of degree n can have at most this many turning points.
What is n-1?
When dividing a polynomial P(x) by (x - k), the remainder equals this value.
What is P(k)? (Remainder Theorem)
For a complex number a + bi, this related complex number is a - bi.
What is the complex conjugate?
This occurs in the graph of a rational function when a factor can be canceled from both the numerator and denominator.
What is a hole?
If the discriminant b² - 4ac of a quadratic equation is negative, the equation has this many real solutions.
What is zero?
According to the Fundamental Theorem of Algebra, a polynomial equation of degree n has exactly this many solutions, counting multiplicities and complex solutions.
What is n?
When the degree of the dividend is less than the degree of the divisor, this is the quotient.
What is zero?
The result of multiplying i by itself three times (i³) equals this.
What is -i?
This type of asymptote occurs when the degree of the numerator is exactly one more than the degree of the denominator.
What is a slant (or oblique) asymptote?
This form of a quadratic function, f(x) = a(x - h)² + k, directly gives the coordinates of the vertex as (h, k).
What is vertex form?
If a polynomial P(x) has a factor of (x - c)ᵏ, then c is a zero of multiplicity k, and the graph will do this at x = c.
What is touch (but not cross) the x-axis if k is even; cross the x-axis if k is odd?
When using polynomial long division, this term refers to the polynomial that cannot be divided further because its degree is less than the divisor's degree.
What is the remainder?
The modulus or absolute value of the complex number a + bi is calculated using this formula.
What is √(a² + b²)?
To find this type of asymptote for a rational function, divide the numerator by the denominator using polynomial long division.
What is a horizontal or slant asymptote?
For the quadratic function f(x) = ax² + bx + c, the axis of symmetry is given by this formula.
What is x = -b/(2a)?
This theorem states that if P(x) is a polynomial with real coefficients and a + bi is a zero of P(x), then a - bi is also a zero of P(x).
What is the Complex Conjugate Zeros Theorem?
When using synthetic division with the divisor (x - k), the last number in the bottom row represents this.
What is the remainder or P(k)?
When solving x⁴ = 16, there are four solutions. Two are real numbers, and the other two are these complex numbers.
What are 2i and -2i?
For the rational function f(x) = (x² - 9)/(x - 3), the point (3, 6) is this type of feature on the graph.
What is a hole?