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elena55 [62]
3 years ago
11

Writing an Equa

Mathematics
1 answer:
kakasveta [241]3 years ago
6 0

Answer:

Step-by-step explanation:

(3,1) lies below the vertex, so the parabola opens downwards.

Equation for a down-opening parabola with vertex (2,3):

y = a(x-2)² + 3, a<0

Plug in (3,1) and solve for a:

1 = a1² + 3

a  = -2

y = -2(x-2)² + 3

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Below is the graph of y= x.<br> Translate it to make it the graph of y=<br> x-1 + 4.
Oduvanchick [21]
  • First, to shift the graph of y=x 1 unit to the right, so y=x-1
  • Second, to shift the graph of y=x-1 4 units to the left, so y=x-1+4

<h2>Explanation:</h2>

To translate the graph of a function is part of Rigid Transformations because the basic shape of the graph is unchanged

Let \ c \ be \ a \ positive \ real \ number. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:

\bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ h(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ h(x)=f(x)-c

\bullet \ Horizontal \ shift \ c \ units \ to \ the \ right \ \mathbf{right}: \\ h(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ left \ \mathbf{left}: \\ h(x)=f(x+c)

In this case, we have the graph of:

y=x

And we need to translate it to make it the graph of:

y=x-1+4

According to our rules we need:

  • First, to shift the graph of y=x 1 unit to the right, so y=x-1
  • Second, to shift the graph of y=x-1 4 units to the left, so y=x-1+4

But y=x-1+4 is the same as y=x+3, so the previous steps can be simplified as:

  • Shifting the graph of y=x 3 unit to the left.

Below are shown those graphs:

  • The blue one is y=x
  • The red one is y=x-1+4

<h2>Learn more:</h2>

Shifting graphs: brainly.com/question/10010217

#LearnWithBrainly

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First you add 3 and 2 so that is 5 and then you subtract 5 from 9 so the answer is 4.

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