Write each equation in the form y = a(x - h)^2 +k. Identify the vertex, focus, directrix, and axis of symmetry of each parabola. y = -3x^2 - 6x + 7

Deromediqm

Deromediqm

Answered question

2022-07-25

Write each equation in the form y = a ( x h ) 2 + k. Identify the vertex, focus, directrix, and axis of symmetry of each parabola.
y = 3 x 2 6 x + 7

Answer & Explanation

Alanna Downs

Alanna Downs

Beginner2022-07-26Added 11 answers

y = 3 x 2 6 x + 7 = 0
3 x 2 + 6 x = 7
3 ( x 2 + 2 x ) = 7
3 ( x 2 + 2 x + ( .5 2 ) = 7 + 3 ( .5 2 )
3 ( x 2 + 2 x + 1 ) = 10
3 ( x + 1 ) 2 = 10
Answer: y = 3 ( x ( 1 ) ) 2 + 10
Vertex: x = -b/2a = 6/-6 = -1
y = -3 + 6 + 7 = 10
(h,k)= (-1,10)
Focus: y = 1 4 p ( x h ) 2 + k
1 4 p = 3
p=-1/12
= 10 - (1/12) = 9 + 11/12
= (-1, 119/12)
Directrix:
y = 10 + 1/12 = 121/12
Axis of Symmetry:
x = -1

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