Graphing a parabola for a calculus problem

In summary, the conversation discusses graphing a parabola for a calculus problem, specifically how to factor and use the two x values as x-intercepts and determine the turning point. The equation y=4x^2 - 25 is given as an example and the process of factoring and finding the x-intercepts is explained. The formula for finding the turning point is mentioned and the correct coordinates of the vertex are clarified. Help is requested and appreciated.
  • #1
hotrocks007
10
0
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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  • #2
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.
 
  • #3
factoring you get (2x-5) (2x+5) set these equal to zero
 
  • #4
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).
 

FAQ: Graphing a parabola for a calculus problem

How do you identify the vertex of a parabola when graphing for a calculus problem?

The vertex is the point on a parabola where it changes direction. To identify the vertex, use the formula x = -b/2a, where a and b are the coefficients of the quadratic equation. The x-value of the vertex is the midpoint between the two x-intercepts, and the y-value of the vertex can be found by substituting the x-value into the original equation.

How do you determine the direction of opening for a parabola when graphing for a calculus problem?

The direction of opening for a parabola is determined by the leading coefficient, a, in the quadratic equation. If a is positive, the parabola opens upwards and if a is negative, the parabola opens downwards.

What is the significance of the x-intercepts when graphing a parabola for a calculus problem?

The x-intercepts represent the solutions to the quadratic equation and can be found by setting the equation equal to 0 and solving for x. In a calculus problem, the x-intercepts may represent important points such as the maximum or minimum value of a function.

How do you plot points on a parabola when graphing for a calculus problem?

To plot points on a parabola, choose values for x and substitute them into the equation to find the corresponding y-values. These points can then be plotted on the coordinate plane to create the parabola.

Can a parabola have more than one vertex?

No, a parabola can only have one vertex. The vertex is the point where the parabola changes direction, and there can only be one point where this occurs.

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