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.

Practise quadratic functions free

What this topic covers

Worked examples

Example 1

Express x2+6x−5x^2 + 6x - 5 in the form (x−h)2+k(x - h)^2 + k.
Show the worked solution
  • $x^2 + 6x - 5$
  • $= x^2 + 6x + \frac{36}{4} - \frac{36}{4} - 5 \quad \scriptsize\textit{add and subtract }(6/2)^2$
  • $= (x + 3)^2 - 14$
  • $h = -3,\; k = -14$

Answer: "h":"−3","k":"−14"{"h":"-3","k":"-14"}

Example 2

Find the maximum or minimum value of y=3(x−1)(x+1)y = 3(x - 1)(x + 1).
Show the worked solution
  • The $x$-intercepts are $x = 1$ and $x = -1$.
  • $x$-coordinate of turning point $= \dfrac{1 - 1}{2} \quad \scriptsize\textit{average of x-intercepts}$
  • $= 0$
  • $y = 3(0 - 1)(0 + 1)$
  • $= -3$
  • The minimum value is $-3$, occurring when $x = 0$.

Answer: "type":"minimum","value":"−3","xValue":"0"{"type":"minimum","value":"-3","xValue":"0"}

Example 3

Does the curve y=−x2−2x−4y = -x^2 - 2x - 4 lie completely above or below the xx-axis?
Show the worked solution
  • $y = -x^2 - 2x - 4$
  • $= -(x + 1)^2 - 3 \quad \scriptsize\textit{complete the square}$
  • $a = -1 < 0$, so the curve has a maximum value of $-3$.
  • Since the maximum value is negative, the curve lies completely <b>below</b> the $x$-axis.

Answer: belowbelow

Questions parents ask

Is it really free?

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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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