The equation for the curved supporting arch of a bridge (shown in red on the diagram) is given by h = - 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. Determine the range of values of h .

The equation for the curved supporting arch of a bridge (shown in red on the diagram) is given by h = - 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. To determine the range of values of, we have to find the h -intercept by putting x = 0 in the equation h = - 1 40 x - 20 2 then, h = - 1 40 0 - 20 2 h = - 1 40 - 20 2 h = - 1 40 400 h = - 10 Therefore, the range of value of h is - 10 ≤ h ≤ 0 .

The equation for the curved supporting arch of a bridge (shown in red on the diagram) is given by h = - 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?

We have, h = - 1 40 x - 20 2 h = 1 40 - x 2 + 40 x - 400 To sketch the graph Step 1 : x 2 term is negative, so the graph is ∩ 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 = - 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 = - 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 = - - 40 2 1 x = 20 Now substitute x = 20 into the equation to find the h -coordinate of the turning point. h = - 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 .

Karen Morrison & Nick Hamshaw solutions for Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition Curved Graphs Karen Morrison and Nick Hamshaw Solutions for Exercise 3: Exercise 18.3

HARD

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 18 - Curved Graphs>Exercise 18.3>Q 3

Sketch the following graph. Indicate the axis of symmetry and the coordinate of the turning point on the graph.

y = 1 + 2 x - 2 x^{2}

HARD

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 18 - Curved Graphs>Exercise 18.3>Q 3

Sketch the following graph. Indicate the axis of symmetry and the coordinate of the turning point on the graph.

$y = - {(x + 2)}^{2} - 1$

MEDIUM

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 18 - Curved Graphs>Exercise 18.3>Q 4

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.

Question Image

Determine the turning point of the graph of the relationship.

EASY

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 18 - Curved Graphs>Exercise 18.3>Q 4

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.

Question Image

What are the possible values for $x$ ?

EASY

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 18 - Curved Graphs>Exercise 18.3>Q 4

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.

Question Image

Determine the range of values of $h$ .

HARD

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 18 - Curved Graphs>Exercise 18.3>Q 4

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.

Question Image

Sketch a graph of the equation within the possible values.

HARD

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 18 - Curved Graphs>Exercise 18.3>Q 4

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.

Question Image

What is the width of the supporting arch?

EASY

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 18 - Curved Graphs>Exercise 18.3>Q 4

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.

Question Image

What is the maximum height of the supporting arch?

Karen Morrison and Nick Hamshaw Solutions for Exercise 3: Exercise 18.3

Karen Morrison Mathematics Solutions for Exercise - Karen Morrison and Nick Hamshaw Solutions for Exercise 3: Exercise 18.3

Questions from Karen Morrison and Nick Hamshaw Solutions for Exercise 3: Exercise 18.3 with Hints & Solutions

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