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Mathematics

2 answers:

sergeinik [125]3 years ago

8 0

The answer is c.

The -3 means it’s shifted to the right 3 units
The 4 means it shifted up 4 units

Olin [163]3 years ago

3 0

For this case we have the following function:
f (x) = x ^ 2
We have the following information:
Horizontal translations
Suppose that h> 0
To graph y = f (x-h), move the graph of h units to the right
f (x) = (x-3) ^ 2
Vertical translations
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units up.
f (x) = (x-3) ^ 2 + 4
Answer:
f (x) = (x-3) ^ 2 + 4
option C

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Write a quadratic equation with the given roots. Write the equation in the form of ax^2+bx+c=0 where a b and c are integers

Bas_tet [7]

You haven't provided the required roots, but I can tell you how to do this kind of exercises in general.

If the $x^2$ coefficient is 1, i.e. the equation is written like $x^2+bx+c=0$ , then you can say the following about the coefficients b and c:

$b$ is the opposite of the sum of the roots
$c$ is the multiplication of the roots.

So, for example, if we want an equation whose roots are 4 and -2, we have:

$4+(-2) = 4-2 = 2 \implies b = -2$
$4 \cdot (-2) = -8 \implies c = -8$

So, the equation is $x^2-2x-8=0$

If your roots are rational, you can work like this: suppose you want an equation with roots 3/4 and 1/2. You have:

$\dfrac{3}{4}+\dfrac{1}{2} = \dfrac{3}{4}+\dfrac{2}{4} = \dfrac{5}{4} \implies b = -\dfrac{5}{4}$
$\dfrac{3}{4} \cdot \dfrac{1}{2} = \dfrac{3}{8} \implies c = \dfrac{3}{8}$