Name: Non-linear Graphs
Uploaded: 2019-07-19
Duration: 4 min 41 s
Description: Here's an introduction to the graphs of four non-linear functions: quadratic, cubic, square root, and absolute value. Let us watch this video and understand the concept.

Question

The equation for the curved supporting arch of a bridge (shown in red on the diagram) is given by $h = - \frac{1}{40} {(x - 20)}^{2}$ where $h m$ is the distance below the base of the bridge and $x m$ is the distance from the left side.

What is the width of the supporting arch?

Accepted Answer

We have,

$h = - \frac{1}{40} {(x - 20)}^{2}$

$h = \frac{1}{40} (- x^{2} + 40 x - 400)$

To sketch the graph

Step $1$ : $x^{2}$ term is negative, so the graph is $\cap$ shaped

Step $2$ : By making $x = 0$ in the equation,

$h = - 10$

Then, $h$ -intercept $= (0, - 10)$

Step $3$ : By making $h = 0$ in the equation,

$0 = - \frac{1}{40} {(x - 20)}^{2}$

$0 = {(x - 20)}^{2}$

$0 = x - 20$

Then, $x = 20$

So, $(20, 0)$ is the $x$ -intercept

Step $4$ : We know that when the equation is in standard form $y = a x^{2} + b x + c$ , the axis of symmetry can be found by using $x = - \frac{b}{2 a}$ .

We can write $40 h = - x^{2} + 40 x - 400$ as

$- 40 h = x^{2} - 40 x + 400$

Then the $x$ -coordinate of the turning point.

Then, $x = - \frac{- 40}{2 (1)}$

$x = 20$

Now substitute $x = 20$ into the equation to find the $h$ -coordinate of the turning point.

$h = - \frac{1}{40} {(20 - 20)}^{2}$

$h = 0$

Then the turning point is $(20, 0)$

Clearly from the diagram the width pf the supporting arch is $40 m$ .

$x$	$20$	$40$	$60$	$80$	$100$	$40 m$
$y$	$12$		$4$			$2$

$x$	$- 3$	$- 2$	$- 1$	$0$	$1$	$2$
$y = - x^{2} - x + 1$	$- 5$	$- 1$	$1$	$1$	$- 1$	$- 5$

The equation for the curved supporting arch of a bridge (shown in red on the diagram) is given by $h = - \frac{1}{40} {(x - 20)}^{2}$ where $h m$ is the distance below the base of the bridge and $x m$ is the distance from the left side.

What is the width of the supporting arch?

Important Questions on Curved Graphs

Learn and Prepare for any exam you want !

The equation for the curved supporting arch of a bridge (shown in red on the diagram) is given byh=-140x-202 where h m is the distance below the base of the bridge and x m is the distance from the left side. What is the width of the supporting arch?

Important Questions on Curved Graphs

Learn and Prepare for any exam you want !

The equation for the curved supporting arch of a bridge (shown in red on the diagram) is given by $h = - \frac{1}{40} {(x - 20)}^{2}$ where $h m$ is the distance below the base of the bridge and $x m$ is the distance from the left side.

What is the width of the supporting arch?