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DiKsa [7]
3 years ago
7

The function f(t) = t2 + 12t − 18 represents a parabola. Part A: Rewrite the function in vertex form by completing the square. S

how your work. (6 points) Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points) Part C: Determine the axis of symmetry for f(t). (2 points)
Mathematics
2 answers:
weeeeeb [17]3 years ago
7 0
Complete the square:
f(t) = t² + 12t - 18, f(t) = (t² +12t) -18. 
Complete the square of t² +12t ↔ t² + 12t + 36 -36 = (t+6)² -36, ten:

f(t) = t² + 12t - 18 = (t+6)² -36 - 18 ↔f(t) = (t + 6)² - 54
f(t) = y = t + 6)² - 54 or ↔ y+54 = (t+6)²
(y+54) = (t+6)² is the standard form of a parabola. [(y-k) = a(x-h)²]
The vertex is (-54,-6) and since a is positive, te parabola opens upward with a minimum (-54,-6)
For the axis of symmetry, let's take again the initial form y= t²+12t-18.
(ax²+bx+c). The axis of symmetry is - b/2a = (-12)/2 = -6.
Then the axis of symmetry is x= -6
Gala2k [10]3 years ago
4 0
Part A:    
f ( t ) = t² + 12 t - 19
( t² + 12 t + 36 ) - 36 - 18
( t + 6)² - 54

Part B : The vertex ( - 6, -54 ).
This is the minimum, because the parabola is open up ( a > 0 ).

Part C : The axis of symmetry t = - 6.
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Artist 52 [7]

Answer:

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Step-by-step explanation:

y-2 = -3(x-5)

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7 0
3 years ago
9/10 = z/8 round to the nearest tenth
jeka57 [31]
9/10 = z/8

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72 = 10z

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3 years ago
Sophia determined that the expression Negative (4 x minus 5) + 2 (x minus 3) is equivalent to –2x – 5 by using the steps below.
CaHeK987 [17]

Answer:Hope This Helps ☺️

Step-by-step explanation:

She is not correct because she did not substitute the same number in both expressions in Step 1

Step-by-step explanation:

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L.H.S

-(4x-5)+2(x-3)

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R.H.S

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Hence for x= 1

-(4x-5)+2(x-3) ≠ -2x -5

Because -3 ≠ -7

CASE 2: substitute -1 for x to both sides of the equations

L.H.S

-(4x-5)+2(x-3)

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R.H.S

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-(4x-5)+2(x-3) ≠ -2x -5

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Answer:

She is not correct because she did not substitute the same number in both expressions in Step 1

3 0
3 years ago
Read 2 more answers
The given line passes through the points (−4, −3) and (4, 1).
deff fn [24]

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\dfrac{y_2-y_1}{x_2-x_1}.

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\dfrac{1-(-3)}{4-(-4)}=\dfrac{4}{8}=\dfrac{1}{2}.

Two perpendicular lines have slopes that form product of -1, then the slope of perpendicular line is -\dfrac{1}{\frac{1}{2}}=-2.

The  line that passes through the point (−4, 3) and has slope -2 has equation:

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3 0
4 years ago
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If the length of side of square is 3x-y,what is the area of the square in terms of x.and y?
shtirl [24]

Answer:

\large\boxed{A=9x^2-6xy+y^2}

Step-by-step explanation:

The formula of an area of a square:

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7 0
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