Question

How to solve worded quadratic problems?

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

Answer 1

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`

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