Using the completing-the-square method, find the vertex of the function f(x) = 5x2 + 10x + 8 and indicate whether it is a minimum or a maximum and at what point. a. maximum (1,8) b. minimum (1,8) c. maximum (-1,3) d. minimum (-1,3)

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The vertex form is a(x-h)²+k, where (h,k) are the coordinates of the vertex. [latex]f(x)= \\ 5x^2+10x+8= \\ 5(x^2+2x)+8= \\ 5((x^2+2x+1)-1)+8= \\ 5((x+1)^2-1)+8= \\ 5(x+1)^2-5+8= \\ 5(x+1)^2+3[/latex] The coordinates of the vertex are (-1,3). The coefficient of x² is positive, so the parabola opens upwards and the vertex is the minimum of the function. The answer is d.

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