Exam 1

Question 1

What is the quadratic formula?

Answer 1

x = (-b ± √(b² - 4ac)) / (2a)

Question 2

True or False: The sum of the roots of a quadratic equation ax² + bx + c = 0 is given by -b/a.

Answer 2

True

Question 3

Fill in the blank: The vertex of a parabola given by the equation y = ax² + bx + c can be found at the point (____, ____).

Answer 3

( -b/2a, f(-b/2a) )

Question 4

What is the standard form of a linear equation?

Answer 4

y = mx + b

Question 5

What does ‘m’ represent in the linear equation y = mx + b?

Answer 5

The slope of the line

Question 6

What is the y-intercept in the equation y = mx + b?

Answer 6

The value of y when x = 0, represented by ‘b’.

Question 7

Simplify: (3x² + 5x) + (4x² - 2x).

Answer 7

7x² + 3x

Question 8

True or False: A function can have multiple outputs for a single input.

Answer 8

False

Question 9

What is the domain of the function f(x) = 1/x?

Answer 9

All real numbers except x = 0.

Question 10

What is the result of factoring the expression x² - 9?

Answer 10

(x - 3)(x + 3)

Question 11

What is the definition of a polynomial?

Answer 11

An expression consisting of variables raised to whole number exponents and coefficients.

Question 12

Multiple Choice: What is the degree of the polynomial 4x³ - 3x² + 2?

Answer 12

A) 2 B) 3 C) 1 D) 0

Question 13

What is the leading coefficient in the polynomial 5x⁴ - 2x³ + 3?

Answer 13

5

Question 14

True or False: The discriminant of a quadratic equation determines the nature of its roots.

Answer 14

True

Question 15

What is the discriminant in the quadratic equation ax² + bx + c?

Answer 15

b² - 4ac

Question 16

Fill in the blank: A system of equations can be solved using the ____ method, substitution method, or graphing.

Answer 16

elimination

Question 17

What is the formula for the slope between two points (x₁, y₁) and (x₂, y₂)?

Answer 17

m = (y₂ - y₁) / (x₂ - x₁)

Question 18

What is the result of the expression 2(x + 3) - 4?

Answer 18

2x + 2

Question 19

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.

Answer 19

B) X-values can repeat

Question 20

What is the term for the highest power of a variable in a polynomial?

Answer 20

Degree

Question 21

True or False: The graph of a linear equation is always a straight line.

Answer 21

True

Question 22

What is the formula for the area of a rectangle?

Answer 22

Area = length × width

Question 23

Fill in the blank: A rational function is defined as the ratio of two ____.

Answer 23

polynomials

Question 24

What is the vertex form of a quadratic function?

Answer 24

y = a(x - h)² + k

Question 25

What does the variable ‘h’ represent in the vertex form of a quadratic function?

Answer 25

The x-coordinate of the vertex

Question 26

What is the solution to the equation 2x + 3 = 11?

Answer 26

x = 4

Question 27

What type of graph does a quadratic function produce?

Answer 27

A parabola