Question

+ 14" alt="y = x {}^{2} - 9x + 14" align="absmiddle" class="latex-formula">
Given that y can be written in the form
$(x + a) {}^{2} + b$
, where a and b are constants, find the value of a and the value of b.​
pls help i rly need this Pls pls pls pls

Answer 1

Answer:

a = - $\frac{9}{2}$ , b = - $\frac{25}{4}$

Step-by-step explanation:

To obtain the required form use the method of completing the square

add/ subtract ( half the coefficient of the x- term)² to x² - 9x

y = x² + 2(- $\frac{9}{2}$ )x + $\frac{81}{4}$ - $\frac{81}{4}$ + 14

  = (x - $\frac{9}{2}$ )² - $\frac{81}{4}$ + $\frac{56}{4}$

  = (x - $\frac{9}{2}$ )²- $\frac{25}{4}$ ← in the form (x + a)² + b

with a = - $\frac{9}{2}$ and b = - $\frac{25}{4}$

Answer 2

Answer:

a = 4.5

b = -6.25

Step-by-step explanation:

The given equation to us is ,

$\implies y = x {}^{2} - 9x + 14$

And its given that it can we written in the form of ,

$\implies (x + a) {}^{2} + b$

Where ,

• a and b are constants .

Therefore ,

$\implies y = x^2 -9x + 14$

Multiplying 9x by 2/2 ,we have ,

$\implies y = x^2 -\dfrac{2}{2}\times 9 x + 14$

Adding and subtracting (9/2)² ,

$\implies y = \bigg\{ x^2 -\dfrac{2}{2}\times 9 x + \bigg(\dfrac{9}{2}\bigg)^2 \bigg\} +14 -\bigg(\dfrac{9}{2}\bigg)^2$

Therefore , we can write it as ,

$\implies y = \bigg( x + \dfrac{9}{2}\bigg)^2 + 14 - 20.25 \\\\\implies \underline{\underline{ y = \bigg( x + \dfrac{9}{2}\bigg)^2 - 6.25 }}$

Hence the value of a is 9/2 and b is -6.25 .