f(x)= -2x²-8x-5 a.)Express in vertex form b.) Find the zeros of the function c.) Find Y-intercept?

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  • ?
    Lv 6
    2 months ago

    f(x) = -2x² - 8x - 5

    a) 

    -2x² - 8x - 5 = -2 * (x² + 4x + 5/2) = -2 * (x² + 4x + 4 - 4 + 5/2) = 

    = -2 * (x² + 4x + 4 - 3/2) = -2 * [(x + 2)² - 3/2] = -2 * (x + 2)² + 3

    Equation of f(x) in vertex form :

    f(x) = -2 * (x + 2)² + 3 

    b)

    f(x) = 0 ===> -2 * (x + 2)² + 3 = 0 ===> -2 * (x + 2)² = -3 ===> (x + 2)² = 3/2 ===>

    ===> x + 2 = ±√(3/2) ===> x = -2 ± √(3/2) ===> x = -2 ± (√6)/2

    Zeros of f(x) ===> (-2 - (√6)/2; 0) (-2 + (√6)/2; 0)

    c)

    f(0) = f(x = 0) = -2 * 0² - 8 * 0 - 5 = -5

    y-intercept: (0; -5)

  • 2 months ago

    f(x) = -2x² - 8x - 5 => -2(x² + 4x) - 5

    i.e. -2(x + 2)² - 5 + 8

    so, f(x) = -2(x + 2)² + 3

    The zeros occur when f(x) = 0

    i.e. when  -2(x + 2)² + 3 = 0

    so, (x + 2)² = 3/2

    Then, x + 2 = ±√6/2

    i.e. x = -2 ± √6/2

    Hence, zeros at (-2 - √6/2, 0) and (-2 + √6/2, 0)

    y-intercept at x = 0

    so, f(0) = -2(2)² + 3 => -5

    Hence, y-intercept at (0, -5)

    :)>  

  • ?
    Lv 7
    2 months ago

    a. y - 3= -2(x + 2)²

    b. x= -2 +/- √6 /2

    c. (0, -5)

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