Question

Find the vertex, axis of symmetry, domain, and range of the graph of y = −3x2 − 3x + 4

Explain how you can determine the axis of symmetry, the domain, and range without graphing y = −3x2 − 3x + 4.

Answer 1

use \(x=-\frac{b}{2a}\) for your axis of symmetry

Answer 2

in your case \(y=-3x^2-3x+4\) you have \(a=-3,b=-3, -\frac{b}{2a}=-\frac{-3}{2\times (-3)}=-\frac{1}{2}\)

Answer 3

is the axis of symmetry -1/2 ?

Answer 4

yup
well the axis of symmetry is not a number it is a line
the equation for the line is \(x=-\frac{1}{2}\)

Answer 5

equation for a vertical like is \(x=c\) for some constant \(c\)

Answer 6

domain is easiest
it is a polynomial, so domain is all real numbers

Answer 7

so is the range y<= 19/4?

Answer 8

for the range you need to see what you get when you replace \(x\) by \(-\frac{1}{2}\)
since this is a parabola that opens down, the range will be from minus infinity to whatever you get for the \(y\) value at \(x=-\frac{1}{2}\)

Answer 9

you got it!

Answer 10

thanks! can you help with part 2?? @satellite73