Quadratics (Unit 3)

Vertex Form

The vertex form of a quadratic equation is given by:

y = a(x - h)^2 + k

where (h, k) represents the coordinates of the vertex.

Quadratics

Quadratics is a branch of algebra that deals with equations of the form ax^2 + bx + c = 0, where a, b, and c are constants. It involves solving quadratic equations, graphing parabolas, and analyzing their intercepts.

Parabola

A parabola is a U-shaped curve that can be defined by a quadratic equation. It is a conic section and is symmetric about its axis of symmetry. The general equation of a parabola is y = ax^2 + bx + c, where a, b, and c are constants. The vertex of the parabola is the point where it reaches its minimum or maximum value.

Axis of Symmetry

The axis of symmetry is a vertical line that divides a symmetrical shape into two equal halves.

Equation: -b/2a

X-Intercepts

The x-intercepts of a function are the points where the graph intersects the x-axis. They are also known as the roots or zeros of the function. To find the x-intercepts, set the function equal to zero and solve for x.

Y-Intercepts

The y-intercept is the point where a graph intersects the y-axis. It represents the value of the dependent variable (y) when the independent variable (x) is equal to zero.