Question

How can we find vertex of degree 4 polynomials​

Answer 1

The vertex of a degree 4 polynomial involves more complex steps than a quadratic equation, requiring factoring or calculus if possible. For a simple quadratic equation, the vertex can be found using the formula -b/(2a) for the x-coordinate.

Step-by-step explanation:

Finding the vertex of a degree 4 polynomial is not as straightforward as finding the vertex of a quadratic function. However, if the polynomial can be factored into quadratic equations or if its derivative can be found, you may then identify the critical points which could lead you to the vertex - if it exists. A vertex in the context of a degree 4 (quartic) polynomial would be any local maxima or minima.

For quadratic equations of the form at² + bt + c = 0, finding the vertex is simpler as it is given by the formula –b/(2a) for the x-coordinate, and then substituting this into the equation to find the y-coordinate. For a quadratic equation with constants a = 4.90, b = 14.3, and c = -20.0, we apply the quadratic formula for finding the roots, and the vertex can be found using the mentioned formula for the x-coordinate.

Answer 2

Below

Step-by-step explanation:

Everywhere there is a local max or minima, the slope = 0

IF you take the first derivative, set it = 0 and solve for the x values, you will get these local max/min points ....but you will not know if they are a max or a min....

so take the SECOND derivative and sub in each of the values that you got ......if you get a POSITIVE result it is a min.... a negative result is a max point...... when you find the min point(s) ...use that value of 'x' in the original equation to find the corresponding 'y' coordinate.....

OR: You can graph the function to SEE the min points .....