Algebraic Reasoning - Solving Linear & Quadratic Word Problems

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive slope means it rises, negative slope means it falls).

Front

How do you write an equation from a word problem?

Back

Identify the variables, determine the relationship between them, and translate the words into mathematical expressions or equations.

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the second degree, typically in the form ax² + bx + c = 0, where a, b, and c are constants.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How do you find the roots of a quadratic equation?

Back

The roots of a quadratic equation can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if it's positive, there are two real roots; if it's zero, there is one real root; if it's negative, there are no real roots.

Front

What does it mean for a function to be modeled by a quadratic equation?

Back

It means that the relationship between the variables can be represented by a parabola, which can describe various real-world scenarios like projectile motion.

Front

How do you interpret the coefficients in a quadratic function?

Back

The coefficient 'a' affects the width and direction of the parabola, 'b' affects the position of the vertex, and 'c' represents the y-intercept.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. Solutions to the system are the points where the equations intersect.