Precalc unit 3 notes

Vertex The highest or lowest point of a parabola. Found using the formula x = -b/2a.

Axis of Symmetry An invisible line that cuts a parabola in half. It passes through the vertex.

Quadratic Function An equation in the form y = ax² + bx + c, which graphs as a parabola.

Parabola A U-shaped curve that represents a quadratic function.

Y-Intercept The point where the graph crosses the y-axis (set x = 0).

X-Intercepts The points where the graph crosses the x-axis (set y = 0).

Maximum Value If the parabola opens downward (frown ☹), the vertex gives the highest value.

Minimum Value If the parabola opens upward (smile 😊), the vertex gives the lowest value.

Vertex Form The equation y = a(x - h)² + k, where (h, k) is the vertex.

Standard Form The equation y = ax² + bx + c, used for finding the axis of symmetry.

Solving Quadratic Inequalities Graph the parabola, then shade above or below depending on the inequality sign.

Dashed vs. Solid Line Use a dashed line for < or >. Use a solid line for ≤ or ≥.