Question 10 (3 marks):
Diagram shows the graph y = a (x – p)2 + q, where a, p and q are constants. The straight line y = –8 is the tangent to the curve at point H.
Diagram
(a) State the coordinates of H.
(b) Find the value of a.
Solution:
(a)
(b)
Diagram shows the graph y = a (x – p)2 + q, where a, p and q are constants. The straight line y = –8 is the tangent to the curve at point H.
![](http://spmaddmaths.blog.onlinetuition.com.my/wp-content/uploads/sites/3/2018/12/Picture56.png)
(a) State the coordinates of H.
(b) Find the value of a.
Solution:
(a)
(b)
Question 11 (3 marks):
Faizal has a rectangular plywood with a dimension 3x metre in length and 2x metre in width. He cuts part of the plywood into a square shape with sides of x metre to make a table surface.
Find the range of values of x if the remaining area of the plywood is at least (x2 + 4) metre2.
Solution:
![](http://spmaddmaths.blog.onlinetuition.com.my/wp-content/uploads/sites/3/2018/12/Picture58.png)
Area of plywood – area of square ≥ (x2 + 4)
3x(2x) – x2 ≥ x2 + 4
6x2 – x2 – x2 ≥ 4
4x2 ≥ 4
x2 – 1 ≥ 0
(x + 1)(x – 1) ≥ 0
x ≤ –1 or x ≥ 1
Thus, x ≥ 1 (length is > 0)
![](http://spmaddmaths.blog.onlinetuition.com.my/wp-content/uploads/sites/3/2018/12/Picture57.png)
Faizal has a rectangular plywood with a dimension 3x metre in length and 2x metre in width. He cuts part of the plywood into a square shape with sides of x metre to make a table surface.
Find the range of values of x if the remaining area of the plywood is at least (x2 + 4) metre2.
Solution:
![](http://spmaddmaths.blog.onlinetuition.com.my/wp-content/uploads/sites/3/2018/12/Picture58.png)
Area of plywood – area of square ≥ (x2 + 4)
3x(2x) – x2 ≥ x2 + 4
6x2 – x2 – x2 ≥ 4
4x2 ≥ 4
x2 – 1 ≥ 0
(x + 1)(x – 1) ≥ 0
x ≤ –1 or x ≥ 1
Thus, x ≥ 1 (length is > 0)
![](http://spmaddmaths.blog.onlinetuition.com.my/wp-content/uploads/sites/3/2018/12/Picture57.png)