Algebra 2 EOC

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect on a graph.

To find the solution graphically, plot each equation on the same graph and identify the point(s) where the lines intersect.

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola. It can be found using the formula $$x = -\frac{b}{2a}$$ .

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

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. For the quadratic equation $$y = ax^2 + bx + c$$ , it is given by $$x = -\frac{b}{2a}$$ .

A function has two solutions when its graph intersects the x-axis at two distinct points, indicating two different x-values for which the function equals zero.

The slope of a line measures its steepness and direction, calculated as the change in y divided by the change in x (rise over run). It is represented as $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ .

An undefined slope indicates a vertical line, where the x-values are constant and the line does not rise or fall.

To represent an inequality graphically, draw the boundary line (solid for <= or >=, dashed for < or >) and shade the region that satisfies the inequality.

A strict inequality (< or >) does not include the boundary line, while a non-strict inequality (<= or >=) includes the boundary line.