5-2 Properties of Quadratic Functions in Standard Form

Vertex of: g(x) = 2(x + 2)2 +4

(-2,4)

Vertex of: f(x) = x2

(0,0)

Vertex of: k(x) = x2 - 5

(0,5)

Standard Form (Definition)

A way of writing down very large or very small numbers easily. 103 = 1000 and 4 × 103 = 4000 .

Where the Vertex lies on

Axis of Symmetry

(x,y)

Could be any point on the graph

The first step in finding the axis of symmetry

Find the (h,k) values

(h,k)

Is the point of the vertex on a parabola

Quadratic Function (Definition)

One of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.

a is negative

Parabola opens downwards

a is positive

Parabola opens upwards

Axis of Symmetry (Definition)

The line through the vertex of a parabola that divides the parabola into two congruent halves.

Standard Form of a Quadratic Equation (Formula)

f(x) = ax^2 + bx + c

A Formula that the Axis of Symmetry correlates with

x=b/2a

Vertex Form of a Parabola (Formula)

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