Systems: Quadratic and Linear

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system of equations graphically?

Back

It means to find the point(s) where the graphs of the equations intersect.

Tags

CCSS.8.EE.C.8B

Front

What is a linear equation?

Back

An equation that forms a straight line when graphed, typically in the form y = mx + b.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is a quadratic equation?

Back

An equation that can be expressed in the form ax² + bx + c = 0, where a, b, and c are constants.

Front

What is the vertex of a parabola?

Back

The highest or lowest point of the parabola, depending on its orientation.

Front

How do you find the vertex of a quadratic function in standard form?

Back

Use the formula x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

What is the discriminant in a quadratic equation?

Back

The value of b² - 4ac, which determines the nature of the roots.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean if the discriminant is positive?

Back

The quadratic equation has two distinct real roots.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean if the discriminant is zero?

Back

The quadratic equation has exactly one real root (a repeated root).

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean if the discriminant is negative?

Back

The quadratic equation has no real roots, only complex roots.

Tags

CCSS.HSA-REI.B.4B