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igomit [66]
3 years ago
9

Using graph paper, determine the line described by the given point and slope. Click to show the correct graph below.

Mathematics
1 answer:
gayaneshka [121]3 years ago
7 0

When you know the coordinates of a point and the slope of a line, you can use the formula

y-y_0=m(x-x_0)

in your case, (x_0,y_0)=(0,0) and m=\frac{2}{3}, so you have

y-0=\dfrac{2}{3}(x-0) \iff y=\dfrac{2}{3}x

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The parent function f(x)=x^2 is translated such that the function g(x)=-x^2+6x-5 represented the new function. What is true abou
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<h3>Answer:</h3>
  • g(x) has an axis of symmetry at x = 3
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<h3>Step-by-step explanation:</h3>

The vertex form of g(x) is ...

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You know the leading coefficient is -1 because that's what it is for x² in the given form. When you factor -1 from the first two terms, of the given form, you have ...

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<em>About transformations</em>

g(x) = f(x -a) causes the graph of f(x) to be shifted "a" units to the right. For a function f(x) with an axis of symmetry at x=0, it moves the axis of symmetry to x=a.

g(x) = f(x) +a causes the graph of f(x) to be shifted "a" units up.

g(x) = -f(x) causes the graph of f(x) to be reflected across the x-axis.

Here, we have all three of these transformations. First is the reflection:

... f₁(x) = -f(x) = -x²

Then we have shifting to the right 3 units. (also moves the axis of symmetry)

... f₂(x) = f₁(x-3) = -(x -3)²

Finally, we have shifting up 4 units.

... g(x) = f₂(x) +4 = -(x -3)² +4

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