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Lena [83]
2 years ago
14

Y=4 times 1/2 to the power of x i need help putting it into a table

Mathematics
1 answer:
timama [110]2 years ago
3 0

Answer:

Step-by-step explanation:

y=4 times 1/2 to the power of x can be written symbolically as

                                                             4                  4

y = 4(1/2)^x.  This is the same as y = ------- or y = -------- * 2^(-x)

                                                             2^x                1

This function is a "decaying exponential."

A suitable table follows:

x      4(2^[-x])         x    y

0      4(2^0)           (0, 4)

1        4(2^1)            (1, 8)

2       4(2^2)           (2, 16)

and so on.

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Rewrite the equation in vertex form. then find the vertex of the graph. y=-3x^2-5x+1
amm1812

Answer: y = -3(x + \frac{5}{6})² + \frac{37}{12}, (-\frac{5}{6}, \frac{37}{12})

<u>Step-by-step explanation:</u>

First, you need to complete the square:

y   = -3x² - 5x + 1

<u> -1  </u>   <u>                -1  </u>

y - 1 = -3x² - 5x

y - 1 = -3(x² + \frac{5}{3}x

y - 1 + -3(\frac{25}{36}) = -3(x² + \frac{5}{3}x + \frac{25}{36})

           ↑                     ↓            ↑

                                  \frac{5}{3*2} = (\frac{5}{3*2})^{2}

y - 1 - \frac{25}{12} = -3(x + \frac{5}{6})²

y - \frac{12}{12} - \frac{25}{12} = -3(x + \frac{5}{6})²

y  - \frac{37}{12} = -3(x + \frac{5}{6})²

y = -3(x + \frac{5}{6})² + \frac{37}{12}

Now, it is in the form of y = a(x - h)² + k   <em>where (h, k) is the vertex</em>

Vertex = (-\frac{5}{6}, \frac{37}{12})

8 0
3 years ago
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