Quadratic Word Problems

Front

What is a quadratic equation?

Back

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

Front

What does it mean to solve a quadratic equation?

Back

To solve a quadratic equation means to find the values of the variable (usually x) that make the equation true.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph of a quadratic function, depending on its orientation.

Front

How do you find the axis of symmetry of a parabola?

Back

The axis of symmetry of a parabola given by the equation y = ax² + bx + c is x = -b/(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 positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

What is a word problem in mathematics?

Back

A word problem is a mathematical problem expressed in words, requiring translation into a mathematical equation to solve.

Front

How do you set up a quadratic equation from a word problem?

Back

Identify the variables, translate the relationships and conditions into an equation, and express it in the standard form ax² + bx + c = 0.

Front

What is the area of a rectangle?

Back

The area of a rectangle is calculated by multiplying its length by its width (Area = length × width).

Front

How do you find the length of a rectangle if the area and width are known?

Back

To find the length, divide the area by the width (Length = Area / Width).