Options A. 1/49 B.1/14 C.49 D.14

Mathematics

1 answer:

grigory [225]3 years ago

5 0

$\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 7^{-\frac{5}{6}}\cdot 7^{-\frac{7}{6}}\implies 7^{-\frac{5}{6}-\frac{7}{6}}\implies 7^{\frac{-5-7}{6}}\implies 7^{\frac{-12}{6}}\implies 7^{-2}\implies \cfrac{1}{7^2}\implies \cfrac{1}{49}$

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A parabola is given by the equation y = x2 + 4x + 4.

notsponge [240]

Answer:

the vertex of the parabola is:(-2,0)

the focus of the parabola is:(-2, $\frac{1}{4}$ )

the directrix of the parabola is:y= $\frac{-1}{4}$

Step-by-step explanation:

we know that for any general equation of the parabola of the type $y=ax^{2} +b x+c$ the vertex of the parabola is given by (h,k)

where $h=\frac{-b}{2 a}$ and $k=\frac{4 a c-b^{2} }{4a}$

therefore by the given data we have h=-2 and k=0

hence vertex=(-2,0)

the general equation of the parabola of the type $4 a (y-h)=(x-k)^2$ ; the parabola symmetric around the y-axis has the focus from the centre i.e. the vertex (h,k) at a distance a as (h,k+a) and the directrix is given by y=k-a