Please help I’ll mark you

9514 1404 393

  A.  f(x) = (x -3)² -1

  B.  vertex: (3, -1); axis of symmetry: x=3; x-intercepts: {2, 4}; y-intercept: 8

  C.  see attached for a graph

Step-by-step explanation:

A. Put the function in vertex form by completing the square. Start by putting parentheses around the terms containing x.

  f(x) = (x² -6x) +8

Now, identify the coefficient of x (-6) and square half of that. (-6/2)² = 9. Add this value inside parentheses, and subtract this value outside parentheses.

  f(x) = (x² -6x +9) +8 -9

Rewrite the trinomial in parentheses as a square. The constant in the binomial will be the value you squared in the previous step.

  f(x) = (x -3)² -1 . . . . . vertex form; a(x -h)²+k for vertex (h, k)

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B. The vertex and the axis of symmetry can be read from the equation. Here, the vertex is (3, -1). The axis of symmetry is the vertical line through the vertex: x = 3. The x-intercepts are found by solving f(x) = 0.

  f(x) = 0

  (x -3)² -1 = 0

  (x -3)² = 1 . . . . . add the opposite of the 'k' value

  x -3 = ±√1 . . . . take the square root. We need both signs.

  x = 3 ± 1 . . . . . add 3 to get x by itself. These are the x-intercepts.

  x = 3-1 = 2  and  x = 3+1 = 4

The x-intercepts are 2 and 4, points (2, 0) and (4, 0).

The y-intercept is the value of f(0). It is the constant in the original form of the function. f(0) = 8 . . . . y-intercept

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C. The graph is attached. The various points above are marked, and the axis of symmetry is shown.

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?

i believe the correct answer is option 4.principalities were small territories that were run by russian rulers.

which statement correctly defines principalities in northern asia in the 1200s? principalities were small territories that were run by russian rulers.

hope i could ! : )