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f(x) = x^2 + 10x + 24
=(x^2 + 10x)+ 24
=(x^2 + 10x + 25 - 25) + 24
f(x) =(x+5)^2 - 1

Vertex: (-5, -1)

How do you sketch this? I know that in the graph one of the coord is (-5, -1) but how do I find the others in order to make a parabola? :|

  • math -

    Factorize to get the zeroes:
    f(x)=x²+10x+24=(x+6)(x+4)
    Therefore the zeroes at at x=-6, x=-4.

    The y-intercept is y=24 (= constant term)
    The coefficient of x² is positive, so the curve is concave upwards.

    The vertex is the minimum of the parabola, and x=-5 passing through the vertex is the axis of symmetry.

    That should give enough information to sketch the graph?

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