How to solve worded quadratic problems?

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can someone please explain to me how to do question 2c)? Thank you so much!

1 Answer
Mar 21, 2017

Answer:

Answering question part 2c

Yes! The tcaravan will fit.

Explanation:

Set y to the value of 2 (height of caravan ) and calculate the horizontal distance between the points of the curve at that height (#x# value).

#color(purple)("Height if the caravan is 2 metres so:")#

#color(purple)(ul(bar(|color(white)(2/2)"Set "y=2=-0.3125x^2+2.5xcolor(white)(2/2)|))#

Subtract 2 from both sides giving

#0=-0.3125x^2+2.5x-2#

Now solve as a quadratic.

Given the standardised form of:

#y=ax^2+bx+c# where #x=(-b+-sqrt(b^2-4ac))/(2a)#

#a=-0.3125"; "b=2.5"; "c=-2#

Once you have the difference between the two values of #x# compare this to the width of the vehicle.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Completed the calculation due to a query") #

So at the caravan's height of 2 meters the x-coordinates are:

#x=(-2.5+-sqrt((2.5)^2-4(-0.3125)(-2)))/(2(-0.3125))#

As we have #-b+-sqrt(...# The #+-# bit must mean that the point #b# is the centre about which you have the #+-# bit. So the width of the opening at the height of 2 metres is" #" "cancel(2)xx(sqrt((2.5)^2-4(-0.3125)(-2)))/(cancel(2)(-0.3125)) = 9.295... metres#

Tony B

The trailer is 5 metres wide so this will fit that gap with an approximate total sideways clearance of 4.3 metres.

Approximately 2.15 metres clearance either side