GA milestone Algebra 1 Unit 5

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

How do you graph an inequality like y > -2x + 3?

Back

To graph y > -2x + 3, first graph the line y = -2x + 3 as a dashed line (since it's not inclusive). Then shade the area above the line.

Front

What does the vertex of a parabola represent?

Back

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

Front

How do you find the vertex of the function f(x) = (x + 3)² + 5?

Back

The vertex of f(x) = (x + 3)² + 5 is at the point (-3, 5). This is derived from the standard form of a parabola, f(x) = a(x - h)² + k, where (h, k) is the vertex.

Front

What does it mean for a function to be shifted?

Back

A function is shifted when its graph is moved horizontally or vertically without changing its shape. For example, f(x) = (x + 3)² + 5 is shifted 3 units left and 5 units up from the parent function f(x) = x².

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

Front

How do you determine the direction of shading for an inequality?

Back

To determine the direction of shading, test a point not on the line (usually (0,0) if it's not on the line) in the inequality. If the inequality holds true, shade the side of the line that includes that point.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What is the significance of the coefficients in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0), while 'b' affects the position of the vertex and 'c' represents the y-intercept.

Front

How do you solve a system of inequalities?

Back

To solve a system of inequalities, graph each inequality on the same coordinate plane and identify the region where the shaded areas overlap.