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Compare the parabola describes by each equation with the standard parabola describes by the equation y = x^2. In your answer, include transformations, the position of the vertex, and the equation of the axis of symmetry.
a) y = 3x^2 - 8
b) y = (x - 6)^2+4
c) y = -4(x+3)^2 - 7
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Hi :) to do this question, firstly we have to understand what a standard parabola is. I suggest you read up on it: http://www.clausentech.com/lchs/dclausen/algebra2/parabolas.htm
Now, we want a nice equation in the form ax^2 + bx + c. So I suggest you simplify the terms in options a, b and c so that you get something along that form. For example, a) is already in that form. b) will be x^2 - 12x +36 + 4, which in other words is x^2 - 12 x +40.
Next will be plotting the graphs. You might want to use an online graph plotting application to do so :) Then plot one graph on top of another and there you go! You will then be able to compare the graphs :) Hope this helped, have a nice day!