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3 years ago

(-($(+(+&((-(-((+(&(4//4/&(&(/+/$

Mathematics

1 answer:

kondor19780726 [428]3 years ago

7 0

So what is the question

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Express the function f(x) =3x^2-6x-18 in the form a(x + h)^2=k, where a, h and k are constants.Hence state the :

ololo11 [35]

Answer:

The minimum value of f(x) is -21 and it occurs at x = 1

Step-by-step explanation:

f(x) =3x^2-6x-18

Factor out the greatest common factor out of the first two terms

f(x) =3(x^2-2x)-18

Complete the square

-2x/2 =-1 (-1)^2 = 1

Add 1 (But remember the 3 out front so we are really adding 3 so we need to subtract 3 to remain balanced)

f(x) = 3(x^2 -2x+1) -3 -18

f(x) = 3(x-1)^2 -21

This is vertex form

f(x) = a(x-h)^2 +k where (h,k) is the vertex and a is a constant

The vertex is (1,-21)

Since a > 0 this opens upward and the vertex is a minimum

The minimum value of f(x) is -21 and it occurs at x = 1

6 0

3 years ago

Triangle ABC is rotated to create the image A'B'C

Alborosie

Is there more to this?

3 0

3 years ago

Read 2 more answers

Choose the inequality that could be used to solve the following problem.

hjlf

Hmm, I think your answer would be 3x ≥ -6

Let me know if this helps!

6 0

4 years ago

Plot the vertex and the axis of symmetry of this function on the provided graph. f(x) = (x + 2)2 − 6

Nookie1986 [14]

Answer:

See attached image

Step-by-step explanation:

This equation for a parabola is given in vertex form, so it is very simple to extract the coordinates of its vertex, by using the opposite of the number that accompanies the variable "x" in the squared expression (opposite of 2) for the vertex's x-value, and the value of the constant (-6) for the vertex's y-value.

The vertex coordinates are therefore: (-2,-6)

The equation of the axis of symmetry of the parabola is a vertical line passing through the vertex. Since all vertical lines have the shape x = constant in our case, in order to pass through (-2,-6) the vertical line is defined by the equation: x = -2.

See image attached to find the vertex drawn as a red point, and the axis of symmetry as an orange vertical line passing through it.

3 0

3 years ago

Janet's home went to Citizens Bank she borrowed 7000 at a rate of 8% the date of the alone was September 20th Janet Hope to repa

almond37 [142]

Interest depends a lot on the compounding period.
Since the period is exactly 4 months, we assume
APR=8%
monthly interest=8/12%=0.00666667
Interest due in 4 months
=7000[(1+0.08/12)^4-1]
=7000[0.0269345]
=$188.54

6 0

3 years ago