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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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.

Tags

CCSS.HSA.REI.C.7

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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.

Tags

CCSS.HSA-REI.B.4B

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.