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3 years ago

What is the vertex of the graph of the function below? y = x2 + 8x + 12

1 answer:

5 0

Hello,

$The\,\,formula\,\,for\,\,the\,\,vertex\,\,of\,\,a\,\,quadratic\,\,equation\,\,is: \\ V=( -\frac{b}{2a},f(-\frac{b}{2a}) )$

That means that we must first obtain x, then we replace x in the function to get y, so:

$x=- \frac{b}{2a} \\ \\ x=- \frac{8}{2*(1)} \\ \\ \boxed{x=-4} \\ \\ Reeplacing \,\,x: \\ y=(-4)^{2} +8*(-4)+12 \\ y=16-32+12 \\ \boxed{y=-4}$

Answer: V=(-4 , -4)

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Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2 and the profit

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Changing the equation into slope form: $y = mx + c$ , where $m$ is the slope [gradient] and $c$ is the y-intercept.

$2x+3y=1470$
$3y = -2x+1470$
$y= - \frac{2}{3}x+ \frac{1470}{3}$
$y=- \frac{2}{3}x+490$

The gradient is $- \frac{2}{3}$ and y-intercept is at $y=490$

Graphing $y=- \frac{2}{3}x+490$ using slope-intercept method:
a) The slope is a negative slope. The line will go 'down hill'
b) The line must pass the point (0, 490)
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The graph of this function is shown below. The intercepts are labelled at:
y = 490
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Next month's profit equation

$2x+3y=1593$

Rewriting this into slope-equation form

$3y = -2x+1593$
$y=- \frac{2}{3}+ \frac{1593}{3}$
$y= - \frac{2}{3}+531$

The gradient, $m$ , equals to $- \frac{2}{3}$
The y-intercept, $c$ , equals to 531

The equation still has the same gradient with last month's profit equation but different y-intercept.

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A linear graph show points of (0, 300) and (450, 0)

We work out the slope:
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Y-intercept at x = 0, so it's at y = 300

Equation $y = - \frac{2}{3}+300$

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3 years ago

Write an recursive formula for An, the nth term of the sequence<br> 5, -2, -9,

oksian1 [2.3K]

Given:

The given sequence is:

$5,-2,-9,...$

To find:

The recursive formula for $a_n$ , the nth term of the sequence.

Solution:

We have,

$5,-2,-9,...$

Here, the first term is 5.

$-2-5=-7$

$-9-(-2)=-9+2$

$-9-(-2)=-7$

The common difference is -7.

The recursive formula for the nth term of the sequence is

$a_n=a_{n-1}+d$

Where, $d$ is the common difference.

Putting $d=-7$ in the above formula, we get

$a_n=a_{n-1}+(-7)$

$a_n=a_{n-1}-7$

Therefore, the recursive formula for the nth term of the sequence is $a_n=a_{n-1}-7$ .

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Answer:

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Step-by-step explanation:

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