9.5 - Solving systems with linear and quadratic functions

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation 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 function?

Back

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

Front

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

Back

To find the intersection, set the equations equal to each other and solve for x. Then substitute x back into either equation to find y.

Tags

CCSS.HSA.REI.C.7

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, meaning it makes all equations true when substituted.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, found using the formula x = -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.

Tags

CCSS.HSA-REI.B.4B

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Tags

CCSS.HSA-REI.B.4B

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that the quadratic equation has no real roots, only complex roots.

Tags

CCSS.HSA-REI.B.4B

Front

What does a zero discriminant indicate?

Back

A zero discriminant indicates that the quadratic equation has exactly one real root, also known as a repeated root.

Tags

CCSS.HSA-REI.B.4B