6.1 Quadratic Linear Systems

Front

What is a quadratic-linear system?

Back

A system of equations that includes one quadratic equation and one linear equation.

Tags

CCSS.HSA.REI.C.7

Front

What does it mean if a quadratic-linear system has no solutions?

Back

It means that the graphs of the equations do not intersect at any point.

Tags

CCSS.HSA.REI.C.7

Front

How can you determine the number of solutions in a quadratic-linear system?

Back

By analyzing the graphs of the equations or using algebraic methods to find intersection points.

Tags

CCSS.HSA.REI.C.7

Front

What is the general form of a quadratic equation?

Back

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

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 significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the number of real solutions: if >0, two solutions; =0, one solution; <0, no solutions.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean for a system to have two solutions?

Back

It means that the graphs of the equations intersect at two distinct points.

Tags

CCSS.8.EE.C.8B

Front

How can you solve a quadratic-linear system graphically?

Back

By plotting both equations on the same graph and identifying the points of intersection.

Tags

CCSS.HSA.REI.C.7

Front

What is the y-intercept of a linear equation?

Back

The point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.