What is the factored form of the quadratic expression $$9x^2 - 9x + 2$$ ?

The factored form is $$\left(3x-2\right)\left(3x-1\right)$$ .

How do you find the vertex of a parabola given by the equation $$y = ax^2 + bx + c$$ ?

The vertex can be found using the formula $$x = -\frac{b}{2a}$$ .

What is the formula for the slope of a line given two points (x1, y1) and (x2, y2)?

The slope is given by $$m = \frac{y2 - y1}{x2 - x1}$$ .

What is the standard form of a linear equation?

The standard form is $$Ax + By = C$$ where A, B, and C are integers.

What is the discriminant of a quadratic equation and what does it indicate?

The discriminant is $$b^2 - 4ac$$ ; it indicates the nature of the roots: if > 0, two real roots; if = 0, one real root; if

What is the relationship between the slopes of perpendicular lines?

The slopes of perpendicular lines are negative reciprocals of each other.

What is the formula for the area of a triangle?

The area is given by $$A = \frac{1}{2} \times base \times height$$ .

What is the Pythagorean theorem?

In a right triangle, $$a^2 + b^2 = c^2$$ , where c is the hypotenuse.

What is the definition of a function?

A function is a relation that assigns exactly one output for each input.

Midterm Math 3 (Fall 2024) Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

Back

2.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

3.

FLASHCARD QUESTION

Front

Solve the equation using the square root method: (x+4)^2 - 81 = 0.

Back

The solutions are x = -13 and x = 5.

4.

FLASHCARD QUESTION

Front

What is the slope of a line parallel to a line with slope m = 3/4?

Back

The slope of a parallel line is also 3/4.

5.

FLASHCARD QUESTION

Front

What are the solutions to the system of equations: 7x - 5y = 38 and 2x + 10y = -12?

Back

The solutions are x = 4 and y = -2.

6.

FLASHCARD QUESTION

Front

What is the definition of a quadratic equation?

Back

7.

FLASHCARD QUESTION

Front

What is the zero product property?

Back

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