# Point (p, 4p²) on Curve y = 4x² for All p

• MASH4077
In summary, to show that the point (p, 4p^2) lies on the curve y = 4x^2 for all real values of p, you can substitute p into the equation and see that it satisfies the equation. This means that (p, 4p^2) is on the graph.
MASH4077
Show that the point $$(p, 4p^{2})$$ lies on the curve $$y = 4x^{2}$$ for all real values of p.

I'm not at all sure how to go about answering this. I know that substituting p into $$y = 4x^{2}$$ satisfies the equation. Is that enough?, or I'm not looking at this deep enough. Any hint(s) appreciated.

Thanks.

Saying a point is on the graph given by some equation, you are saying the x- and y-coordinates satisfy that equation. So yes, since substituting x = p into your equation gives y = 4p^2, you know that $(p, 4p^2)$ is on the graph.

Looks like the question wasn't as difficult as I thought it was going to be.

P.S. Appologies to moderators. I'll post these sorts of questions in the correct section next time. ;)

## 1. What is the equation of the curve y = 4x²?

The equation of the curve is y = 4x², which is a quadratic function. This means that the graph of the curve will be a parabola.

## 2. What is the significance of the point (p, 4p²) on the curve?

The point (p, 4p²) is significant because it is a point that lies on the curve y = 4x² for any value of p. This means that for any value of p that is plugged into the equation, the point (p, 4p²) will be a solution to the equation.

## 3. How does the value of p affect the position of the point (p, 4p²) on the curve?

The value of p affects the position of the point (p, 4p²) on the curve by determining the x-coordinate of the point. As p increases, the x-coordinate will also increase, resulting in a point that is further to the right on the curve.

## 4. Is the point (p, 4p²) the only point on the curve y = 4x² for any given value of p?

No, the point (p, 4p²) is not the only point on the curve for any given value of p. There are infinitely many points on the curve, as it is a continuous function. However, the point (p, 4p²) is a special point that will always lie on the curve for any value of p.

## 5. How can the equation y = 4x² be used to find the coordinates of other points on the curve?

The equation y = 4x² can be used to find the coordinates of other points on the curve by plugging in different values for x and solving for y. For example, if x = 2, then y = 4(2)² = 16. This means that the point (2, 16) lies on the curve. By plugging in various values for x, we can find the coordinates of other points on the curve.

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