# How to solve worded quadratic problems?

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

Mar 21, 2017

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).

$\textcolor{p u r p \le}{\text{Height if the caravan is 2 metres so:}}$

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

$0 = - 0.3125 {x}^{2} + 2.5 x - 2$

Given the standardised form of:

$y = a {x}^{2} + b x + c$ where $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$a = - 0.3125 \text{; "b=2.5"; } c = - 2$

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

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$\textcolor{b l u e}{\text{Completed the calculation due to a query}}$

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

$x = \frac{- 2.5 \pm \sqrt{{\left(2.5\right)}^{2} - 4 \left(- 0.3125\right) \left(- 2\right)}}{2 \left(- 0.3125\right)}$

As we have -b+-sqrt(... The $\pm$ bit must mean that the point $b$ is the centre about which you have the $\pm$ bit. So the width of the opening at the height of 2 metres is" $\text{ } \cancel{2} \times \frac{\sqrt{{\left(2.5\right)}^{2} - 4 \left(- 0.3125\right) \left(- 2\right)}}{\cancel{2} \left(- 0.3125\right)} = 9.295 \ldots m e t r e s$

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