Question

The vertex of a parabola is (3,2). A second point on the parabola is (1,5). Which of the following points is also on the graph?
(3,7)

(5,5)

(3,-2)

(-1,5)

Answer 1

if we use the vertex form of a parabola, that is http://nayak2010.files.wordpress.com/2011/01/picture-of-vertex-form-of-parabola.png

we would end up with \(\bf y = a(x-3)^2+2\)
now, what's is "a"? well, we dunno

but we know that another point in the parabola is (1, 5), so let's use that in our "vertex form" equation
\(\bf y = a(x-3)^2+2\qquad \qquad (1,5)\\ \quad \\
1=a(5-3)^2+2\implies -1=4a\implies -\cfrac{1}{4}=a\\ \quad \\ \quad \\
\textit{so our parabola equation is}\qquad y = -\cfrac{1}{4}(x-3)^2+2\)

now check the points given, see which "x" produces the accompanying "y" in the pair :)

Answer 2

If b^p =N, then which of the following statements is also true?

\[\log_{b}N = p \]

\[\log_{p}N = b\]

\[\log_{n} b = p\]

\[N^\frac{ 1 }{ b } = p\]

Please hurry and help.