Solving Systems: Linear and Quadratic Functions

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for a point to be a solution to a system of equations?

Back

A point is a solution if it satisfies all equations in the system.

Front

How do you determine if a point is a solution to a linear equation?

Back

Substitute the x and y values of the point into the equation and check if the equation holds true.

Front

What is the general form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a quadratic function?

Back

A function that can be expressed in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How do you find the vertex of a quadratic function?

Back

The vertex can be found using the formula x = -b/(2a) and then substituting x back into the function to find y.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is given by b² - 4ac and determines the nature of the roots of the quadratic equation.

Front

What does it mean if the discriminant is positive?

Back

There are two distinct real roots for the quadratic equation.

Front

What does it mean if the discriminant is zero?

Back

There is exactly one real root (a repeated root) for the quadratic equation.

Front

What does it mean if the discriminant is negative?

Back

There are no real roots; the roots are complex or imaginary.