Determine the vertex of each quadratic function. State the equation of the axis of symmetry, the minimum or maximum value, domain and range for each y=10x^2+5x-1, and y=-24x^2+18x+11  

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To determine the vertex, use the formula -b/2a to find the x-value, where in the first equation, b is 5 and a is 10, and 18 and -24 respectively in the second.  So we have vertices with x-values:x1 = -5/(2*10) or -1/4 and x2 = -18/(-2*24) or 3/8.  To find the y-values just plug these numbers into their equations and solve for y:y1 = 10*(-1/4)^2 + 18*(-1/4) + 11y2 = -24*(3/8)^2 + 18*(3/8) + 11(just plug these into your calculator)Then, the axes of symmetry are just the lines x = x1 and x = x2 for each equation. (or x = -1/4 for the first, x = 3/8 for the second)Finally, the domain is everything (-inf, inf) for both equations, and the range is everything above the y-value you found for the vertex in the first equation (y1, inf), and everything below the y-value you found in the second equation (-inf, y2).  This is because the coefficients on the x^2 term are positive or negative, making the parabola face down or up.  In this case up for the first equation, down for the second.