Algebra: Concepts and Connections EOC Review 2

What is a system of inequalities?

• A set of two or more inequalities that share the same variables, with the solution being the set of all points that satisfy all inequalities in the system.

• A single inequality that represents a range of values.

• A collection of equations that have no solutions.

• A method to solve linear equations using graphical representation.

How do you represent a budget constraint in inequalities?

• A budget constraint can be represented as an equation where the total cost is equal to the budget.

• A budget constraint can be represented as an inequality where the total cost must be greater than or equal to the budget.

• A budget constraint can be represented as an inequality where the total cost must be less than or equal to the budget.

• A budget constraint can be represented as a function that shows the relationship between income and expenses.

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

• It represents the slope of the line.

• It is the point where the line crosses the x-axis.

• It is the point where the line crosses the y-axis. It is represented by the value of y when x = 0.

• It indicates the maximum value of the function.

How do you convert a quadratic equation to vertex form?

• By factoring the equation into linear factors.

• By using the quadratic formula to find the roots.

• By completing the square or using the vertex formula.

• By graphing the equation and identifying the vertex.

What is the relationship between the coefficients and roots of a quadratic equation?

• The sum of the roots is given by @@-b/a@@ and the product of the roots is given by @@c/a@@.

• The sum of the roots is given by @@b/a@@ and the product of the roots is given by @@-c/a@@.

• The sum of the roots is given by @@a/b@@ and the product of the roots is given by @@c/b@@.

• The sum of the roots is given by @@-c/a@@ and the product of the roots is given by @@b/a@@.

What is the importance of the slope in a linear equation?

• It represents the y-intercept of the equation.

• It indicates the steepness and direction of the line.

• It shows the maximum value of the dependent variable.

• It determines the number of solutions to the equation.

How do you determine if a point lies on a line represented by an equation?

• Substitute the x-value into the equation and check if the resulting y-value matches the y-coordinate of the point.

• Calculate the distance from the point to the line and see if it is zero.

• Check if the x-coordinate of the point is equal to the slope of the line.

• Determine if the point is within the bounds of the line segment.

What does the vertex form of a quadratic equation look like?

• @@f(x) = a(x-h)^2 + k@@, where (h, k) is the vertex of the parabola.

• @@f(x) = ax^2 + bx + c@@, where a, b, and c are constants.

• @@f(x) = a(x + h)^2 + k@@, where (h, k) is the vertex of the parabola.

• @@f(x) = a(x - h)^2 - k@@, where (h, k) is the vertex of the parabola.

What does it mean for a function to be in standard form?

• A quadratic function is in standard form when it is expressed as @@f(x) = ax^2 + bx + c@@, where a, b, and c are constants.

• A function is in standard form when it is expressed as @@f(x) = mx + b@@, where m and b are constants.

• A function is in standard form when it is expressed as @@f(x) = a(x - h)^2 + k@@, where h and k are constants.

• A function is in standard form when it is expressed as @@f(x) = a^2 + b^2@@, where a and b are constants.

What is the significance of the discriminant in a quadratic equation?

• It determines the coefficients of the equation.

• It indicates the number of solutions: two real roots if positive, one real root if zero, and no real roots if negative.

• It provides the vertex of the parabola.

• It calculates the area under the curve.