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 ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you find the intersection of a linear and a quadratic equation?

Back

To find the intersection, set the linear equation equal to the quadratic equation and solve for x. Substitute the x-values back into either equation to find the corresponding y-values.

Front

What does it mean to solve a system of equations?

Back

Solving a system of equations means finding the values of the variables that satisfy all equations in the system simultaneously.

Front

What is substitution in solving equations?

Back

Substitution is a method where you solve one equation for one variable and then substitute that expression into another equation.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the point where the graph changes direction. It can be found using the formula (-b/2a, f(-b/2a)).

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 roots; if zero, one real root; if negative, no real roots.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has a constant rate of change and graphs as a straight line, while a quadratic function has a variable rate of change and graphs as a parabola.

Front

How can you graph a linear equation?

Back

To graph a linear equation, identify the y-intercept (b) and use the slope (m) to find another point. Draw a straight line through these points.