You are given f(x) = -5x^2 + 10x -5.

a) Express the function in factored form and determine the vertex.

b) Identify the zeros, the axis of symmetry, and the direction of opening.

c) State the domain and range.

d) Graph the function.

Graph and state the max or min value.

a) \displaystyle f(x) = -2x^2 -8x + 3

b) \displaystyle f(x) = 3(x -1)(x + 5)

You can choose whether you are provided the equation of a quadratic function in standard form, factored form, or vertex form. If you needed to know the information listed, which form would you choose and why?

a) the vertex

b) the y-intercept

c) the zeros

d) the axis of symmetry

e) the domain and range

Determine the maximum area of a rectangular field that can be enclosed by 2400 m of fencing.

Determine the equation of the inverse of f(x) =2(x -1)^2 -3.

Simplify

\displaystyle (2-\sqrt{8})(3 + \sqrt{2})

Simplify

\displaystyle (3 + \sqrt{5})(5 -\sqrt{10})

Calculate the value of k such that kx^2 - 4x + k = 0 has one root.

Does the linear function g(x) = 6x -5 intersect the quadratic function f(x) = 2x^2 -3x+2? How can you tell? If it does intersect, determine the point(s) of intersection.

Determine the equation in standard form of the parabola shown below.