Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y)(x,y) point. y=-3x^2+48x-195<

Question

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y)(x,y) point.
y=-3x^2+48x-195

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Aaliyah 2 weeks 2021-10-03T23:45:52+00:00 1 Answer 0

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    2021-10-03T23:47:24+00:00

    Answer:

    (8,-3)

    Step-by-step explanation:

    The given parabola is

    y =  - 3 {x}^{2}  + 48x  - 195

    We factor -3 from the first two terms to get:

    y =  - 3( {x}^{2}   - 16x)  - 195

    Add and subtract the square of half the coefficient of x

    y =  - 3( {x}^{2}   - 16x + 64)   + 3 \times 64- 195

    y =  - 3 {(x - 8)}^{2}  + 192 - 195

    We simplify to get:

    y =  - 3 {(x - 8)}^{2}  - 3

    We compare this to y=a(x-h)²+k,

    The vertex is (h,k)=(8,-3)

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