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Finding the Minimum Value and Sketching a Quadratic Function

The mathematical solution explains how to find the minimum value and sketch the curve of y = 4x2 + 12x + 10. The first method uses calculus, differentiating the function and equating the differential to zero. The resulting equation is solved to find the x value of the minimum point. This value is then substituted into the function to find the y value of the minimum point.

The second method finds the minimum point by expressing the function in completed square format which in this case is a complicated example. Once the completed square form is found, the video explains how to find the minimum point. The explanation moves on to show how to find the point of intersection with the y axis by substituting x = 0 into the equation of the curve. The curve is then sketched using the information found.

The graphical solution explains how to use the graphic calculator to draw the graph of y = 4x2 + 12x + 10, how to change the scale of the axes on the display, how to find the minimum value and the point of intersection of the graph with the y axis.

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