What is the quotient (2x^2 + 12x +18 ) divided by (x +3)

Mathematics

1 answer:

katen-ka-za [31]2 years ago

6 0

2(x^2+6x+9) = 2(x+3)^2

So after divided by (x+3), answer will be:

2(x+3)

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What is the range of the function f(x) = 3x2 + 6x – 8?

timama [110]

Answer:

Range is {y | y ≥ –11}

Step-by-step explanation:

This is quadratic equation.

<em>A quadratic equation's range can be found if we find the vertex.</em>

For quadratic equations that have a positive number in front of $x^{2}$ , it is upward opening and thus <u>all the numbers greater than or equal to the minimum value of vertex is the range.</u>

The formula for vertex of a parabola is:

Vertex = $(-\frac{b}{2a}, f(-\frac{b}{2a})$

Where,

$a$ is the coefficient of $x^{2}$
$b$ is the coefficient of $x$

From our equation given, $a=3$ and $b=6$

Now, $x$ coordinate of vertex is $x=-\frac{b}{2a}\\x=-\frac{6}{(2)(3)}\\x=-\frac{6}{6}\\x=-1$

$y$ coordinate of the vertex IS THE MINIMUM VALUE that we want. We get this by plugging in the $x$ value [ $x=-1$ ] into the equation. So we have: