Express $4x^{2}+8x-5$ in the form $p(x+q)^{2}+r$ , where $p$ , $q$ and $r$ are constants to be found. Hence, state the coordinates of the turning point of the curve $y=4x^{2}+8x-5$ .

Completing the square 中文

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Worked solution

1(i)

1. Factorise the coefficient of $x^2$ from the first two terms

$4x^{2}+8x-5 = 4(x^{2}+2x)-5$

2. Complete the square inside the bracket

$= 4\left[ (x+1)^{2} - 1^{2} \right] - 5$

3. Expand and simplify to reach the final form

$= 4(x+1)^{2} - 4 - 5 = 4(x+1)^{2} - 9$

Answer

$4(x+1)^{2}-9$

1(ii)

1. Identify the turning point from the completed square form found in part (i)

From part (i), $y = 4(x+1)^2 - 9$ .
The minimum value of $y$ occurs when $x+1 = 0$ , which gives $x = -1$ .
The minimum value is $y = -9$ .
Therefore, the coordinates of the turning point are $(-1, -9)$ .

Answer

$(-1, -9)$

AI analysis — may contain mistakes.

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Express 4x2+8x−54x^{2}+8x-54x2+8x−5 in the form p(x+q)2+rp(x+q)^{2}+rp(x+q)2+r, where ppp, qqq and rrr are constants to be found. Hence, state the coordinates of the turning point of the curve y=4x2+8x−5y=4x^{2}+8x-5y=4x2+8x−5.

Worked solution

1(i)

1(ii)

More questions on this topic

Express $4x^{2}+8x-5$ in the form $p(x+q)^{2}+r$ , where $p$ , $q$ and $r$ are constants to be found. Hence, state the coordinates of the turning point of the curve $y=4x^{2}+8x-5$ .