Exam 1 Flashcards
What is the quadratic formula?
x = (-b ± √(b² - 4ac)) / (2a)
True or False: The sum of the roots of a quadratic equation ax² + bx + c = 0 is given by -b/a.
True
Fill in the blank: The vertex of a parabola given by the equation y = ax² + bx + c can be found at the point (____, ____).
( -b/2a, f(-b/2a) )
What is the standard form of a linear equation?
y = mx + b
What does ‘m’ represent in the linear equation y = mx + b?
The slope of the line
What is the y-intercept in the equation y = mx + b?
The value of y when x = 0, represented by ‘b’.
Simplify: (3x² + 5x) + (4x² - 2x).
7x² + 3x
True or False: A function can have multiple outputs for a single input.
False
What is the domain of the function f(x) = 1/x?
All real numbers except x = 0.
What is the result of factoring the expression x² - 9?
(x - 3)(x + 3)
What is the definition of a polynomial?
An expression consisting of variables raised to whole number exponents and coefficients.
Multiple Choice: What is the degree of the polynomial 4x³ - 3x² + 2?
A) 2 B) 3 C) 1 D) 0
What is the leading coefficient in the polynomial 5x⁴ - 2x³ + 3?
5
True or False: The discriminant of a quadratic equation determines the nature of its roots.
True
What is the discriminant in the quadratic equation ax² + bx + c?
b² - 4ac
Fill in the blank: A system of equations can be solved using the ____ method, substitution method, or graphing.
elimination
What is the formula for the slope between two points (x₁, y₁) and (x₂, y₂)?
m = (y₂ - y₁) / (x₂ - x₁)
What is the result of the expression 2(x + 3) - 4?
2x + 2
Multiple Choice: Which of the following is NOT a characteristic of a function? A) Each input has one output B) X-values can repeat C) Y-values can repeat D) The graph passes the vertical line test.
B) X-values can repeat
What is the term for the highest power of a variable in a polynomial?
Degree
True or False: The graph of a linear equation is always a straight line.
True
What is the formula for the area of a rectangle?
Area = length × width
Fill in the blank: A rational function is defined as the ratio of two ____.
polynomials
What is the vertex form of a quadratic function?
y = a(x - h)² + k
What does the variable ‘h’ represent in the vertex form of a quadratic function?
The x-coordinate of the vertex
What is the solution to the equation 2x + 3 = 11?
x = 4
What type of graph does a quadratic function produce?
A parabola
