Quadratic Equations 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 is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (D = b² - 4ac) determines the nature of the roots of the quadratic equation: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

How do you find the vertex of a parabola represented by a quadratic equation?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))) where f(x) is the quadratic function.

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 set up an equation for a word problem involving area?

Back

Identify the dimensions involved, express them in terms of a variable, and set up the equation based on the area formula.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, e.g., (a + b)² = a² + 2ab + b².

Front

What is the relationship between the roots and coefficients of a quadratic equation?

Back

For a quadratic equation ax² + bx + c = 0, the sum of the roots is -b/a and the product of the roots is c/a.

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, express the quadratic in the form (x - p)(x - q) = 0, then set each factor to zero and solve for x.

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.