A maximum turning point is a turning point where the curve is concave up (from increasing to decreasing ) and f′(x)=0 f ′ ( x ) = 0 at the point.

A Turning Point is a critical time in your life where big decisions could lead to big change, both in work and in life. A Turning Point typically shows up about every 10 years of adult life between ages 18 and 65, but, of course, some experience fewer or more Turning Points and experience them at different times.

The easiest way to find the turning point is when the quadratic is in turning point form (y = a(x – h)2 + k), where (h, k) is the turning point. To get a quadratic into turning point form you need to complete the square.

First, identify the leading term of the polynomial function if the function were expanded. Then, identify the degree of the polynomial function. This polynomial function is of degree 4. The maximum number of turning points is 4 – 1 = 3.

Another way is to use -b/2a on the form ax^2+bx+c=0. This will give the x-coordinate of the turning point or otherwise known as the axis of symmetry. We can then use the x-coordinate to sub back into the equation to solve for the y-coordinate. Combining both coordinates will give the turning point.

The turning point of a graph is where the curve in the graph turns. The turning point will always be the minimum or the maximum value of your graph. The parabola ( the curve) is symmetrical. If we know the x value we can work out the y value!

A turning point can be found by re-writting the equation into completed square form. When the function has been re-written in the form y=r(x+s)2+t, the minimum value is achieved when x=-s, and the value of y will be equal to t.

The vertex is the turning point of the graph. We can see that the vertex is at (3,1) ( 3 , 1 ) . The axis of symmetry is the vertical line that intersects the parabola at the vertex.

To find what type of turning point it is, find the second derivative (i.e. differentiate the function you get when you differentiate the original function), and then find what this equals at the location of the turning points. If it’s positive, the turning point is a minimum.

Cubic functions can have at most 3 real roots (including multiplicities) and 2 turning points. If a root of a polynomial has even multiplicity, the graph will touch the x-axis at the root but will not cross the x-axis.

The turning point is at (h, 0). The graph of y = x4 is translated h units in the positive direction of the x-axis. The general form of quartics of this form is y = a(x − h)4 + k The turning point is at (h, k). When sketching quartic graphs of the form y = a(x − h)4 + k, first identify the turning point.

6 Answers. the general cubic equation is y=ax3+bx2+cx+d. Plug in the coordinates of the points for x and y, and you end up with a system of four equations in four variables, namely a,b,c and d. Hope that helps!

Higher degree

Steps to find the equation of a line from two points:

1. Find the slope using the slope formula.
2. Use the slope and one of the points to solve for the y-intercept (b).
3. Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.

An equation is linear if its graph forms a straight line. This will happen when the highest power of x is “1”. An equation is linear if its graph forms a straight line. This will happen when the highest power of x is “1”.