# What is the vertex of #f(x)=7-x^2#?

##### 4 Answers

The vertex is

Sometimes we have problems with the easier questions because it's not exactly in the form we're used to. Normally for a quadratic, you would complete the square to find the vertex. But this quadratic is already in vertex or standard form:

#f(x)=-(x-0)^2+7#

We can also find the vertex by using the expressions:

#(-b/(2a), f(-b/(2a)))#

Standard form:

#ax^2+bx+c=0#

In this example,

#x=−0/(2(−1))=0/2=0#

#y=f(0)=7−0^2=7#

Same result of

Yes, the vertex is at (0,7), but I would like to address this problem graphically.

The graph of a function

When you consider a graph of a function

Next we transform our function into

We could also use Calculus to solve this question.

We have to recognize that this is a quadratic equation which is just a parabola.

We know that a parabola will have either a maximum or minimum at the vertex.

The derivative of a function is the slope of the tangent line at a specific point on the function.

The derivative or tangent line at the vertex will have a slope of 0.

Set the derivative equal to zero to find the

The

Now substitute in

The vertex is at point