Write the the function $\displaystyle {f{{\left({x}\right)}}}=-{3}{x}^{{2}}-{24}{x}-{49}$ in the form $\displaystyle {f{{\left({x}\right)}}}={a}{\left({x}-{p}\right)}^{{2}}+{q}$

Now $\displaystyle {a}={a}$ so $\displaystyle {a}=$

And $\displaystyle {p}=-\frac{{b}}{{{2}{a}}}$ so $\displaystyle {p}=$

And since $\displaystyle {q}$ is the last parameter to solve we may solve it by substituting any point on the curve: $\displaystyle {\left({0};{c}\right)}$ is the $\displaystyle {y}$-intercept of the curve so:

$\displaystyle =$$\displaystyle {(}$ - $\displaystyle {)}^{{2}}+{q}$

$\displaystyle {q}=$

Therefore:

$\displaystyle {f{{\left({x}\right)}}}=$ Preview Question 6 Part 8 of 8