SAT QOTD - Adv. Alg. - (Monday)

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 solutions to the system are the points where the graphs of the equations intersect.

Front

What are the characteristics of a quadratic equation?

Back

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

Front

How can you determine the number of solutions in a system of equations involving a quadratic and a linear equation?

Back

The number of solutions can be determined by analyzing the intersection points of the graphs of the equations. If they intersect at two points, there are two solutions; if they touch at one point, there is one solution; if they do not intersect, there are no solutions.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for two equations to be consistent?

Back

Two equations are consistent if they have at least one solution. This can occur with either one solution (intersecting lines) or infinitely many solutions (coincident lines).

Front

What is the discriminant of a quadratic equation, and how does it relate to the number of solutions?

Back

The discriminant (D) of a quadratic equation ax^2 + bx + c = 0 is given by D = b^2 - 4ac. It indicates the nature of the roots: if D > 0, there are two distinct real solutions; if D = 0, there is one real solution; if D < 0, there are no real solutions.

Front

What is the vertex of a parabola, and how is it related to a quadratic equation?

Back

The vertex of a parabola is the highest or lowest point on the graph of a quadratic equation. It can be found using the formula (-b/2a, f(-b/2a)).

Front

How do you graph a quadratic equation?

Back

To graph a quadratic equation, identify the vertex, axis of symmetry, and intercepts. Plot these points and draw a smooth curve through them to form a parabola.

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. It can be found using the formula x = -b/(2a).

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x = 0.