Quadratic Word Problems Practice

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in 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 function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola represents the maximum or minimum point of the quadratic function, depending on the direction of the parabola.

Front

How do you find the maximum height of a projectile modeled by a quadratic equation?

Back

The maximum height can be found using the vertex formula t = -b/(2a) in the equation h(t) = at² + bt + c.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

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 does the discriminant of a quadratic equation indicate?

Back

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

Front

How do you determine the area of a rectangle given its length and width?

Back

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

Front

If the width of a rectangle is 5 units less than its length, how can you express the width in terms of length?

Back

Width = Length - 5.

Front

What is the formula for the height of an object in projectile motion?

Back

The height of an object in projectile motion can be modeled by the equation h(t) = -16t² + vt + h₀, where v is the initial velocity and h₀ is the initial height.