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Zepler [3.9K]
3 years ago
8

Please helpp ASAP 2 5 pts + brainliest for best/right answer

Mathematics
1 answer:
dimulka [17.4K]3 years ago
7 0

Answer:

The vertex is at (-3/2, 33/4)

x=-3/2

Step-by-step explanation:

y= -x^2 -3x+6

Factor out a negative from the first two terms

y = -(x^2 +3x)  +6

Complete the square

Take 3 /2  and square it  (3/2)^2  = 9/4

The - on the outside of the parentheses means we really are subtracting it so we need to add it on the outside

y = -(x^2 + 3x + 9/4) +9/4 +6

  = -(x+3/2)^2 + 9/4 +6

Get a common denominator of 4

  = -(x+3/2)^2 + 9/4 +6*4/4

y =- (x+3/2)^2 + 9/4 +24/4

y = -(x+3/2)^2 + 33/4

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

y = -(x - -3/2)^2 + 33/4

The vertex is at (-3/2, 33/4)

The axis of symmetry is at the x coordinate of the vertex

x=-3/2

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Step-by-step explanation:

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Find the vertex of the graph of the function.
lapo4ka [179]

Answer: The correct options are  (1) (5,10), (2) (3,-3), (3) x = -1, (4) y=(x+2)^2+3, (5) 21s and (6) 0, -1, and 5.

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Te standard form of the parabola is,

f(x)=a(x-h)^2+k        .....(1)

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(1)

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h=5 and k=10

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h=3 and k=-3

Therefore, the vertex of the graph is (3,-3) and the fourth option is correct.

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f(x)=4x^2+8x+7

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f(x)=4(x^2+2x+1)+7-4

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y=x^2+4x+7

To make perfect square add (\frac{b}{2a})^2, i.e., 2^2.

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