ALG Unit 7: Quadratic and Linear Systems

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, which means it can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a system of equations to have one solution?

Back

A system of equations has one solution when the graphs of the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solutions?

Back

A system of equations has no solutions when the graphs of the equations are parallel and never intersect.

Front

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

Back

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

Front

How do you solve a system of linear and quadratic equations?

Back

To solve a system of linear and quadratic equations, substitute the linear equation into the quadratic equation and solve for the variable.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by 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 b² - 4ac, which determines the number of solutions.

Front

What are the possible values of the discriminant?

Back

If the discriminant is positive, there are two real solutions; if it is zero, there is one real solution; if it is negative, there are no real solutions.