Question

Express f(x) = -2x² – 7x – 6 in the form k - a(x + h)²​

Answer 1

Answer:

$\frac{37}{2}$ - 2 ( x + $\frac{7}{2}$ )²  

Step-by-step explanation:

a² ± 2ab + b² = ( a ± b )²

~~~~~~~~~~

f(x) = - 2 x² - 7x - 6

- 2 x² - 7x - 6 =

- 2 ( x² + $\frac{7}{2}$ x ) - 6 =

- 2 ( x² + 2 × $\frac{7}{2}$ × x + $\frac{49}{4}$ - $\frac{49}{4}$ ) - 6 =

- 2 ( x + $\frac{7}{2}$ )² + $\frac{49}{2}$ - 6 =

- 2 ( x + $\frac{7}{2}$ )² + $\frac{37}{2}$ =

$\frac{37}{2}$ - 2 ( x + $\frac{7}{2}$ )²  

k = $\frac{37}{2}$

h = $\frac{7}{2}$