# Is the vertex the same as the turning point?

This property is called symmetry. We say that the graph is symmetrical about the y-axis, and the y-axis is called the axis of symmetry. So, the axis of symmetry has equation x = 0. (0, 0) is called the

**turning point**or**vertex**of the parabola.A.

### How do you find the turning point of a curve?

Differentiating an equation gives the gradient at a certain

**point**with a given value of x. To**find turning points**,**find**values of x where the derivative is 0. Thus, there is on**turning point**when x=5/2. To**find**y, substitute the x value into the original formula.#### How do you find the point of inflection?

Then the second derivative is: f "(x) = 6x. Now set the second derivative equal to zero and solve for "x" to**find**possible**inflection points**. which means the function is concave up at x = 1.#### Are stationary points and turning points the same thing?

**Stationary point**is the more general term. Anywhere where the gradient (therefore derivative) of a graph/function is 0, is a**stationary point**. If it is a maximum or minimum, then it is also a**turning point**. However, there is a third type of**stationary point**which is not a**turning point**(max or min).#### What does the first and second derivative tell you?

The**second derivative tells**us a lot about the qualitative behaviour of the graph. If the**second derivative**is positive at a point, the graph is concave up. If the**second derivative**is positive at a critical point, then the critical point is a local minimum. The**second derivative**will be zero at an inflection point.

B.

### What is the turning point of the graph?

This happens because the sign of f(x) changes from one side to the other side of r. there is at most n - 1

**turning points**on the**graph**of f. A**turning point**is a**point**at which the**graph**changes direction.#### Which polynomial function has an end behavior of up and down?

Since the**leading**coefficient of this odd-degree polynomial is positive, then its end-behavior is going to mimic that of a positive cubic. Therefore, the end-behavior for this polynomial will be: "Down" on the**left**and "up" on the right.#### What is the root of a graph?

When we see a**graph**of a polynomial, real**roots**are x-intercepts of the**graph**of f(x). Let's look at an example: The**graph**of the polynomial above intersects the x-axis at (or close to) x=-2, at (or close to) x=0 and at (or close to) x=1.#### What is the degree of the polynomial?

The**degree of a polynomial**is the highest**degree**of its monomials (individual terms) with non-zero coefficients. The**degree**of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer. For example, the**polynomial**which can also be expressed as has three terms.

C.

### What is the turning point in math?

A

**turning point**is a**point**at which the derivative changes sign. A**turning point**may be either a relative maximum or a relative minimum (also known as local minimum and maximum). If the function is differentiable, then a**turning point**is a stationary**point**; however not all stationary**points**are**turning points**.#### What is a power function equation?

Savanna can use her knowledge of**power functions**to create**equations**based on the paths of the comets. A**power function**is in the form of f(x) = kx^n, where k = all real numbers and n = all real numbers. You can change the way the graph of a**power function**looks by changing the values of k and n.#### Which polynomial function has an end behavior of up and down?

Since the**leading**coefficient of this odd-degree polynomial is positive, then its end-behavior is going to mimic that of a positive cubic. Therefore, the end-behavior for this polynomial will be: "Down" on the**left**and "up" on the right.#### What is the turning point in math?

A**turning point**is a**point**at which the derivative changes sign. A**turning point**may be either a relative maximum or a relative minimum (also known as local minimum and maximum). If the function is differentiable, then a**turning point**is a stationary**point**; however not all stationary**points**are**turning points**.

Updated: 3rd December 2019