Section 2.1 Quadratic Functions

Polynomial Function: f(x) = a_nxⁿ + a_n-1x^n-1 + ... + a₁x + a₀

• the coefficients (a_n, a_n-1, ..., a₁, a_{0 ) are all real numbers}
• _{polynomial functons are classified by degrees}

Degree name example 0 constant y=1 1 linear f(x)= 2x+5 2 quadratic h(x)=x^2-x-4 3 cubic y=x^3 4 quartic g(x)=x^4-2x-1 Quadratic Function:

• graphing quadratics

the parent function is , a

nything you add to it will transform the

graph. by changing the coefficient from 1 to 2

it vertically stretches the graph by a unit of two.

Sandard Form of a Quadratic Function:

, the point (h,k) is the vertex of the parabola. the coefficient a shows whether it is opening up or down.(up a>0, down a<0)

• to write a quadratic in standard form, complete the square

Parabola to Sandard From:

• The vertex is also point (h,k), which is (1,1)

is standard form so is the new equation.

solve for a to find the full formula, do this by plugging in a point for f(x) and x.

Maximum and Minimum: use the formula , to find the minimum and maximum points

example:

b=3 and a=-2

the maximum point is .75, it is a maximum because the parabola is facing down.(remember when a is less then 0 it faces down)