Systems of Linear/Quadratics C.F.U.

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 degree two, typically written in the form y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

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

Back

To find the intersection, graph both equations on the same coordinate plane and identify the points where the two graphs intersect.

Front

What does it mean if a system of equations has no solution?

Back

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

Front

What does it mean if a system of equations has one solution?

Back

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

Front

What does it mean if a system of equations has two solutions?

Back

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

Front

How can you determine the number of solutions to a system of equations algebraically?

Back

You can determine the number of solutions by substituting one equation into the other and analyzing the resulting equation for its number of solutions.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola. It can be found using the formula x = -b/(2a) for the x-coordinate.

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

How do you solve a system of equations using substitution?

Back

To solve using substitution, solve one equation for one variable and substitute that expression into the other equation.