Linear / Quadratic Systems of Equations

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the second degree, typically in the form y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

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

Back

A system of equations has no solution when the lines represented by the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have one solution?

Back

A system of equations has one solution when the lines represented by the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have two solutions?

Back

A system of equations has two solutions when the graphs of the equations intersect at two distinct points.

Front

How do you solve a linear-quadratic system of equations?

Back

To solve a linear-quadratic system, substitute the linear equation into the quadratic equation and solve for the variable, then find the corresponding values.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b^2 - 4ac. It determines the nature of the roots: if positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is written as y = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.