47. The equation y = 4.5x² + 9x + 15 describes the height of a diver, in metres, at x seconds.

Change this equation into vertex form by completing the square. State the y-intercept, the equation of the axis of symmetry, and the vertex.

B. Before locating the x-intercepts of the parabola, state the number of roots of the equation.

C. Use the quadratic equation formula to determine the x-intercepts of the parabola when the diver hits the water.

D. Explain why one root is inadmissible. Make a sketch to represent the path of the diver.

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  1. y = 4.5x² + 9x + 15

    4.5 x^2 + 9 x = y - 15

    x^2 + 2 x = (10/45)(y-15)

    x^2 + 2 x +(2/2)^2 = (10/45)(y-15) + 1
    You have a sign error, the height goes to + infinity for large + or - x
    I will lay it out your way but suspect
    h = initial height = 15 m
    Vi = initial speed up = 9 m/s
    4.5 = 9.81/2 = g/2 = half gravity
    h = Hi + Vi t - (g/2)t^2
    is here
    h = 15 + 9 t - 4.9 t^2
    h = 0 is hit the water
    One of your times will be negative, that was before you jumped :)

    but anyway using what you have:

    (x+1)^2 = (10/45)( y-15 ) + (10/45)(45/10)
    (x+1)^2 = (10/45 ( y -15+45/10) = (10/45)(y -10.5)
    vertex at (- 1, 10.5) symmetric about x = -1
    for x axis crossings put y = 0 in
    x+1 = /-(10/45) sqrt (-10.5), imaginary, always above axis of course
    when x = 0, y axis intercept = 15

    now do it right with gravity down :)

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