Graphing a parabola for a calculus problem

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To graph the parabola represented by the equation y=4x^2 - 25, start by factoring to find the x-intercepts, which are at x=2.5 and x=-2.5. The vertex of the parabola is located at the point (0, -25), where the y-value is -25. To determine the turning point, calculate the derivative and set it to zero. Understanding these key points will help in accurately graphing the parabola.
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I am graphing a parabola for a calculus problem. I understand how you factor and use the two x values as your x-intercepts, but I'm not sure how this one would be graphed.

y=4x^2 - 25. I understand how the vertex of the parabola would be at negative 25, but I have no clue what to do woith the 4x^2.
Help would be appreciated. thanks.
 
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Well, like you said factoring and getting the two x-intercepts is a start. You also want to know the turning point. If you don't remember the formula for that, just remember that the derivative is zero at the turning point and solve.
 
factoring you get (2x-5) (2x+5) set these equal to zero
 
By the way, the vertex is not "at negative 25"- that's just the y-value of the point. The vertex is at (0, -25).
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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