3 years ago

Given the quadratic function : f(x)=x^24x-12 Find the vertex. Can you show the steps?!?

1 answer:

6 0

$\bf \textit{vertex of a vertical parabola, using coefficients}
\\\\
\begin{array}{llcccl}
\stackrel{f(x)}{y} = & 1x^2& +4x& -12\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}
\qquad 
\left(-\cfrac{ b}{2 a}\quad ,\quad c-\cfrac{ b^2}{4 a}\right)
\\\\\\
\left(-\cfrac{4}{2(1)}~~,~~-12-\cfrac{4^2}{4(1)} \right)\implies (-2~~,~~-12-4)\implies (-2~~,~~-16)$

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The equation for the pH of a substance is pH = –log[H+], where H+ is the concentration of hydrogen ions. Which equation models t

Elden [556K]

$\bf \textit{Logarithm Cancellation Rules}
\\\\
log_a a^x = x\qquad \qquad \boxed{a^{log_a x}=x}\\\\
-------------------------------\\\\
pH=-log(H+)\qquad \stackrel{pH}{7.2}=-log(H+)\implies -7.2=log_{10}(H+)
\\\\\\
10^{-7.2}=10^{log_{10}(H+)}\implies 10^{-7.2}=H+\implies \cfrac{1}{10^{7.2}}=H+$