Mathematics, 24.02.2021 06:10, erikamaldonado661

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answered: sylvia47

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)

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

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

answered: Guest

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.

answered: Guest

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

$x^2-2x+y^2-6y=26$

we now create space between the x and y terms with parenthesis.

$(x^2-2x)+(y^2-6y)=26$

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

$\frac{-2}{2} =(-1)^{2} =1$

$\frac{-6}{2} =(-3)^{2} =9$

we add the squares to both sides.

$(x^2-2x+1)+(y^2-6y+9)=26+1+9$

simplify.

$(x^2-2x+1)+(y^2-6y+9)=36$

and write the quadratics in factored form.

$(x-1)^{2} +(y-3)^{2} =36$

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

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