Solving Quadratic and Linear Systems

Front

What is a system of linear and quadratic functions?

Back

A system of linear and quadratic functions consists of two equations: one linear (a straight line) and one quadratic (a parabola). The solutions are the points where the two graphs intersect.

Front

What are the possible number of solutions for a system of a linear and a quadratic function?

Back

The possible number of solutions can be 0, 1, or 2. However, there cannot be more than 2 solutions.

Front

How do you find the solution of a system of equations?

Back

To find the solution, you can use substitution or elimination methods, or graph both equations to find their intersection points.

Front

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

Back

No solution means that the graphs of the equations do not intersect; they are parallel lines.

Front

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

Back

One solution means that the graphs of the equations intersect at exactly one point.

Front

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

Back

Two solutions mean that the graphs of the equations intersect at two distinct points.

Front

What is the first step in solving the system: y = x^2 + 3x - 5 and y = x + 3?

Back

The first step is to set the equations equal to each other: x^2 + 3x - 5 = x + 3.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, found at the point (h, k) in the vertex form y = a(x - h)² + k.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root (b² - 4ac) that determines the number of solutions: if > 0, two solutions; = 0, one solution; < 0, no solution.