Quadratic Systems and Word Problems

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 does the vertex of a parabola represent in a quadratic function?

Back

The vertex of a parabola is the highest or lowest point of the graph, representing the maximum or minimum value of the quadratic function.

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 positive, there are two distinct real roots; if zero, there is one real root; if negative, there are no real roots.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables, which can be solved simultaneously.

Front

What does it mean for a system of equations to have no solutions?

Back

A system of equations has no solutions when the equations represent parallel lines that never intersect.

Front

How can you graphically solve a quadratic system?

Back

To graphically solve a quadratic system, plot the equations on the same coordinate plane and identify the points of intersection.

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 is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

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

Back

The maximum height can be found by calculating the vertex of the quadratic equation, using the formula t = -b/(2a) to find the time at which it occurs.