Place the following in standard quadratic form. (which is (x-h)+k ). The find the vertex, axis, domain, range, and zeroes.
(can be all done with a calculator, no work needed.)
1. f(x) = x^2-8x+16
4. f(x)= -x^2+2x+5
5. f(x)= 4x^2-4x+21
6. f(x)= 2x^2-x+1
The standard form is f(x)= ax^2+bx+c . To find the vertex find x-coordinate first using the formula x=-b/2a. The axis is the vertical line with the same x coordinate. Domain is all possible numbers of x you may use, Range is a set of all possible y you are getting by each given formula.To find 0's factor each equation and make it =0, solve it.
I'll do #2 f(x)=16-x^2. Lets rewrite it in standard form -x^2+16, so a=-1, b=0, c=16.
Vertex: x= -b/2a= 0. Plug x=o into y=16-x^2 to find y coordinate of the vertex:y=16, so vertex coordinates are(0,16)
Axis: vertical line x=0(x-axis itself)
Domain: all x's , or x is any real number.
Range is also all real numbers( in #1you would never get negative answer, that's why y>=0)
Zeros: Let's factor it first, -x^2+16=-1(x^2-16)= -1(x-4)(x+4). Make it =0 and solve it, x1=4, x2=-4, so zeros are (4,0), (-4,)