Algebra 2 Midterm Review

A multi-step inequality is an inequality that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, or division.

1. Distribute: $$7 + 3 - 9x < 82$$ 2. Combine like terms: $$10 - 9x < 82$$ 3. Subtract 10: $$-9x < 72$$ 4. Divide by -9 (reverse inequality): $$x > -8$$ .

The parent function of $$y = x^2$$ is the basic quadratic function, which is a parabola opening upwards.

The function shifts left 2 units and down 5 units.

The solution set is $$(-6, \, \, \text{∞})$$ .

1. Find $$p(0) = 6(0) - 2 = -2$$ . 2. Find $$q(0) = -3(0)^2 + 2(0) + 1 = 1$$ . 3. The product is $$q(0) \, p(0) = 1 \, (-2) = -2$$ .

The graph of an inequality represents all the solutions that satisfy the inequality, often shaded to indicate the solution set.

Strict inequalities (<, >) do not include the boundary points, while non-strict inequalities (≤, ≥) do include the boundary points.

Draw a number line, place an open circle at -6, and shade to the left to indicate all numbers less than -6.

The vertex is the highest or lowest point of the parabola, representing the maximum or minimum value of the function.