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dolphi86 [110]
3 years ago
8

What are the coordinates of the vertex of the function f(x) = x2 - 12x + 5?

Mathematics
1 answer:
FinnZ [79.3K]3 years ago
6 0

Answer:

The vertex is the point (6,-31)

Step-by-step explanation:

we have

f(x)=x^2-12x+5

This is a vertical parabola open upward

The vertex represent a minimum

Convert to vertex form

Complete the square

f(x)=(x^2-12x+6^2)+5-6^2

f(x)=(x^2-12x+36)-31

Rewrite as perfect squares

f(x)=(x-6)^2-31 -----> equation in vertex form

therefore

The vertex is the point (6,-31)

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The quotient, which is 1, will be your whole number part of your mixed number. The remainder, 141, will become the numerator of the fraction part of your mixed number. The original denominator of your improper fraction, 859, is still the denominator of your mixed number. So your mixed number form of your improper fraction is:
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3 years ago
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Now both triangles are 30^\circ-60^\circ-90^\circ, which means there's a convenient ratio between its sides. If the length of the shortest leg is \ell_1, then the length of the longer leg is \ell_2=\sqrt3\ell_1 and the hypotenuse has length \ell_3=\sqrt{{\ell_1}^2+{\ell_2}^2}=2\ell_1.

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