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How do you find the maximum point of a curve?

How do you find the maximum point of a curve?

We learned from the first example that the way to calculate a maximum (or minimum) point is to find the point at which an equation’s derivative equals zero. The derivative of this equation is: -8X + 4 and when -8X + 4 = 0, then X= . 5 and it is at that point where the maximum of the curve is located.

How do you find the maximum and minimum points on a graph?

To see whether it is a maximum or a minimum, in this case we can simply look at the graph. f(x) is a parabola, and we can see that the turning point is a minimum. By finding the value of x where the derivative is 0, then, we have discovered that the vertex of the parabola is at (3, −4).

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What are the coordinates of the vertex of the graph is it a maximum or minimum?

One important feature of the graph is that it has an extreme point, called the vertex. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value.

What is the maximum point?

maximum, In mathematics, a point at which a function’s value is greatest. If the value is greater than or equal to all other function values, it is an absolute maximum. In calculus, the derivative equals zero or does not exist at a function’s maximum point.

How do you find the coordinates of a minimum point on a graph?

Looking at this graph, you can see that the minimum point of the graph is at y = -3. The second way to find the minimum value comes when you have the equation y = ax^2 + bx + c. If your equation is in the form y = ax^2 + bx + c, you can find the minimum by using the equation min = c – b^2/4a.

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How do you find the coordinates of a point given an equation?

To find points on the line y = mx + b,

  1. choose x and solve the equation for y, or.
  2. choose y and solve for x.

How do you find the maximum point on a graph in Excel?

Right click on the Max point, and choose Data Labels. Select the label and choose the Series Name option, so it shows “Max”, and choose the bright blue text color. Format the marker so it’s an 8-point circle with a 1.5-pt matching blue border and no fill. Right click on the Min point, and choose Data Labels.

What are the coordinates of the vertex of the graph?

Get the equation in the form y = ax2 + bx + c. Calculate -b / 2a. This is the x-coordinate of the vertex. To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y.

What are the coordinates of the vertex?

The vertex formula to find the vertex coordinates (h,k)= (-b/2a, -D/4a) from the standard equation y = ax2 + bx + c, where D = b2 – 4ac.

How to convert an equation from rectangular to polar coordinates?

Using figure 10.1.3 as an example, the point shown has rectangular coordinates x = ( − 2) cos ( π / 4) = − 2. This makes it very easy to convert equations from rectangular to polar coordinates. Example 10.1.3 Find the equation of the line y = 3 x + 2 in polar coordinates.

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How do you drag a point in a graph?

You can drag the red point in the graph on the left and the corresponding point on the right will follow. Each point in the plane is associated with exactly one pair of numbers in the rectangular coordinate system; each point is associated with an infinite number of pairs in polar coordinates.

What is the minimum value of a quadratic function?

The minimum value of a quadratic function. Consider the function y = x2 +5x−2 You may be aware from previous work that the graph of a quadratic function, where the coefficient of x2 is positive as it is here, will take the form of one of the graphs shown in Figure 1. Figure 1.

How do you graph a line with two points?

Any line can be graphed using two points. Select two x x values, and plug them into the equation to find the corresponding y y values. Tap for more steps… Find the x-intercept.