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Quadratic Functions

Secondary 3 Additional Math practice

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Quadratic Functions practice questions

Secondary 3 topics from the Additional Mathematics 4049 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

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What this topic covers

Worked examples

Example 1

Express x2+7x−6x^2 + 7x - 6 in the form (x−h)2+k(x - h)^2 + k.
Show the worked solution
  • x2+7x−6x^2 + 7x - 6
  • =x2+7x+494−494−6add and subtract (7/2)2= x^2 + 7x + \frac{49}{4} - \frac{49}{4} - 6 \quad \scriptsize\textit{add and subtract }(7/2)^2
  • =(x+72)2−734= (x + \frac{7}{2})^2 - \frac{73}{4}
  • h=−72,  k=−734h = -\frac{7}{2},\; k = -\frac{73}{4}

Answer: "h":"−7/2","k":"−73/4"{"h":"-7/2","k":"-73/4"}

Example 2

Find the maximum or minimum value of y=−2(x−5)(x+1)y = -2(x - 5)(x + 1).
Show the worked solution
  • The xx-intercepts are x=5x = 5 and x=−1x = -1.
  • xx-coordinate of turning point =5−12average of x-intercepts= \dfrac{5 - 1}{2} \quad \scriptsize\textit{average of x-intercepts}
  • =2= 2
  • y=−2(2−5)(2+1)y = -2(2 - 5)(2 + 1)
  • =18= 18
  • The maximum value is 1818, occurring when x=2x = 2.

Answer: "type":"maximum","value":"18","xValue":"2"{"type":"maximum","value":"18","xValue":"2"}

Example 3

Does the curve y=x2−6x+14y = x^2 - 6x + 14 lie completely above or below the xx-axis?
Show the worked solution
  • y=x2−6x+14y = x^2 - 6x + 14
  • =x2−6x+9−9+14add and subtract (6/2)2= x^2 - 6x + 9 - 9 + 14 \quad \scriptsize\textit{add and subtract }(6/2)^2
  • =(x−3)2−9+14= (x - 3)^2 - 9 + 14
  • =(x−3)2+5= (x - 3)^2 + 5
  • a=1>0a = 1 > 0, so the curve has a minimum value of 55.
  • Since the minimum value is positive, the curve lies completely above the xx-axis.

Answer: above

Questions parents ask

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Which syllabus does this follow?

Additional Mathematics (4049), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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