A Math

A Math (IGCSE)

E Math

E Math (IGCSE)

H1 Math

H2 Math

IB AA HL Math

IB AA SL Math

IB AI HL Math

IB AI SL Math

IP Math

N(A) A Math

N(A) E Math

PSLE

PSLE Foundation Mathematics

Consider the expression $x^2-4x-3$.
Express $x^2-4x-3$ in the form $(x-a)^2-b$.
Hence, solve $x^2-4x-3=0$, giving your answers correct to 2 decimal places.

Express $x^2-4x-3$ in the form $(x-a)^2-b$.

Hence, solve $x^2-4x-3=0$, giving your answers correct to 2 decimal places.

Solving Quadratic Equations by Completing the Square

Sec 3/4 E Math T01-Q25 - Completing the square and solving a quadratic equation

Quadratic Functions, Equations and Inequalities

<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Solve the equation $x^2 - 6x - 13 = 3$ with the different methods:</span></div><ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">by factorisation</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">by completing the square</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">by the quadratic formula</span><span class="inline-marks">[2]</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">Solve the equation $-4x^2 + 4x + 3 = 0$ with the different methods:</span></div><ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">by factorisation</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">by completing the square</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">by the quadratic formula</span><span class="inline-marks">[2]</span></div></li></ol></li></ol>

Solve the equation $x^2 - 6x - 13 = 3$ with the different methods:

Solve the equation $-4x^2 + 4x + 3 = 0$ with the different methods:

Solving Quadratic Equations Using the Quadratic Formula

Factorisation of Quadratic Expressions

IP2 Class Test (May 2025) Q3

<ol class="i-list"><li><div class="list-item-paragraph">Write $2{{x}^{2}}+10x-1$ in the form of $a{{(x+h)}^{2}}-k$.</div></li><li><div class="list-item-paragraph">Hence, solve $2{{x}^{2}}+10x-1=0$.</div></li></ol>

Completing the Square (General Quadratic Form)

<ol class="i-list"><li><div class="list-item-paragraph">Express $6-2x-{{x}^{2}}$ in the form of $p-{{(x-q)}^{2}}$ , where&nbsp;$p$ and $q$ are constants.</div></li><li><div class="list-item-paragraph">Hence, solve the equation $6-2x-{{x}^{2}}=0$ giving your answers correct to $2$ decimal places.</div></li></ol>

Completing the Square with Negative Quadratics

<ol class="i-list"><li><div class="list-item-paragraph">Express ${{x}^{2}}-13x-9$ in the form ${{(x+a)}^{2}}+b$.</div></li><li><div class="list-item-paragraph">Hence solve the equation $2{{x}^{2}}-26x-18=-98$.</div></li></ol>

Completing the Square (General Form)

<ol class="i-list"><li><div class="list-item-paragraph">Express ${{x}^{2}}+4x-6$ in the form ${{\left( x+a \right)}^{2}}+b$ where&nbsp;$a$ and $b$ are integers</div></li><li><div class="list-item-paragraph">Hence, solve the equation ${{x}^{2}}+4x-6=0$.</div></li></ol>

Completing the Square (Integer Form)

<ol class="i-list"><li><div class="list-item-paragraph">Express ${{x}^{2}}-6x-13$ in the form ${{(x-a)}^{2}}-b$, where&nbsp;$a$ and $b$ are integers.</div></li><li><div class="list-item-paragraph">Hence, solve the equation ${{x}^{2}}-6x-13=3$ giving your answers correct to $2$ decimal places.</div></li></ol>

Completing the Square to Solve Quadratic Equations

<p>Solve the following equations by completing the square, giving your answers correct to $2$ decimal places.</p>
<ol class="i-list"><li><div class="list-item-paragraph">${{x}^{2}}+3x-6=0$</div></li><li><div class="list-item-paragraph">${{x}^{2}}-5x-3=0$</div></li><li><div class="list-item-paragraph">$5x-{{x}^{2}}+4=0$</div></li></ol>

Solve the following equations by completing the square, giving your answers correct to $2$ decimal places.

Solving Quadratics by Completing the Square

<ol class="i-list"><li><div class="list-item-paragraph">If&nbsp;$25{{x}^{2}}-30x+{{k}^{2}}$ is a perfect square, find the positive value of $k$.</div></li><li><div class="list-item-paragraph">Hence, solve the equation $25{{x}^{2}}-30x+{{k}^{2}}=5$ giving your answers correct to $2$ decimal places.</div></li></ol>

Perfect Square Quadratics (Advanced Form)

<ol class="i-list"><li><div class="list-item-paragraph">If ${{x}^{2}}+10x+m$ is a perfect square, find the value of $m$.</div></li><li><div class="list-item-paragraph">Hence, solve the equation ${{x}^{2}}+10x+m=0$ giving your answers correct to $2$ decimal places.</div></li></ol>

Perfect Square Quadratics

<figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765438585833-pwwd9xk41kf.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0Mzg1ODU4MzMtcHd3ZDl4azQxa2YucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5Mjg2NzcxMSwiZXhwIjoxNzkyODY4MDExfQ.2ExPC74KcYzz9yC0ZApXTM7mBzOrL1rADGyF2v7mtVU" style="max-width: 600px; height: auto; display: block;" class="aligncenter custom-width" /></figure>
<p>Tip: </p>
<p>Note that the coefficient of ${{x}^{2}}$ in the above form is $1$.</p>
<p>So what happen if the coefficient of ${{x}^{2}}$ is not $1$? </p>
<p>Then divide both sides of the equations by the coefficient of ${{x}^{2}}$ such that this will become $1$.</p>

Note that the coefficient of ${{x}^{2}}$ in the above form is $1$.

So what happen if the coefficient of ${{x}^{2}}$ is not $1$? 

Then divide both sides of the equations by the coefficient of ${{x}^{2}}$ such that this will become $1$.

Tips

<ol class="i-list"><li><div class="list-item-paragraph">Express ${{x}^{2}}+4x+7$ in the form of ${{\left( x+a \right)}^{2}}+b$.</div></li><li><div class="list-item-paragraph">Hence, solve the equation ${{x}^{2}}+4x+7=12$.</div></li></ol>

IP2U4 Exercise Q8

<p>Express $\mathrm{f}\left( x \right)={{x}^{2}}-x-5$ in the form of $y={{(x-h)}^{2}}+k$. Hence, solve $\mathrm{f}\left( x \right)=0$.</p>

Express $\mathrm{f}\left( x \right)={{x}^{2}}-x-5$ in the form of $y={{(x-h)}^{2}}+k$. Hence, solve $\mathrm{f}\left( x \right)=0$.

<p>Express $\mathrm{f}\left( x \right)={{x}^{2}}-6x-10$ in the form of $y={{(x-h)}^{2}}+k$. Hence, solve $\mathrm{f}\left( x \right)=0$.</p>

Express $\mathrm{f}\left( x \right)={{x}^{2}}-6x-10$ in the form of $y={{(x-h)}^{2}}+k$. Hence, solve $\mathrm{f}\left( x \right)=0$.

<p>Express $\mathrm{f}\left( x \right)=\frac{1}{2}{{x}^{2}}+2x-3$ in the form of $f(x)=\frac{1}{2}{{(x-h)}^{2}}+k$. Hence, solve $\mathrm{f}\left( x \right)=0$.</p>

Express $\mathrm{f}\left( x \right)=\frac{1}{2}{{x}^{2}}+2x-3$ in the form of $f(x)=\frac{1}{2}{{(x-h)}^{2}}+k$. Hence, solve $\mathrm{f}\left( x \right)=0$.

Math Question Bank