The parametric equations x = square root t, y= 3t - 4 for t in [ 0,4] define a plane curve

a) We kindly invite you to read the explanation and check the image attached below for further details.

b) The rectangular equation is .

Step-by-step explanation:

a) Let and for . We proceed to graph the expression with the help of a graphing tool. In this case, the tool Desmos is used and the result is presented below.

b) The rectangular equation for the curve is:

(1)

(2)

By applying (1) in (2), we get the following equation in rectangular form:

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1

12

step-by-step explanation:

12 + 5 = 17

12x2=24

24-7=17