Question

How do you graph `y=sqrt(3x+4)`?

Answer 1

This is in fact a quadratic in `y`

See the explanation

Explanation:

Given: `y=sqrt(3x+4)`

Square both sides

`y^2=3x+4` Now we are off!

`x=1/3y^2-4/3`

Compare to `x=ay^2+by+c`

`color(green)("There is no "by" term so the axis of symmetry is the x-axis")`

`color(green)("The x-intercept (vertex) is at "x=-4/3)`

Determine the y-intercepts

`y=(-b+-sqrt(b^2-4ac))/(2a)` where `a=1/3, b=0 and c=-4/3`

`y=(0+-sqrt(0-4(1/3)(-4/3)))/(2(1/3))`

`y=+-sqrt(4^2/3^2)xx3/2`

`y=+-4/3xx3/2 = +-2`