Question

The standard form of the equation of a parabola isy=x²-4x+21. What is the vertex form of the equation?O A. y = ¹/(x-4)² +13OB. y=(x-4)² +21C. y = 1/(x+4)² +1+13O D. y = 1/(x+4)² +21

Answer 1

Step-by-step explanation: We have to find the vertex form of the parabola equation from the given standard form of it:

`y=(1)/(2)x^2-4x+21\rightarrow(1)`

The general form of the vertex parabola equation is as follows:

`\begin{gathered} y=A(x-h)^2+k\rightarrow(2) \\ \\ \text{ Where:} \\ \\ (h,k)\rightarrow(x,y)\Rightarrow\text{ The Vertex} \end{gathered}`

Comparing the equation (2) with the original equation (1) by looking at the graph of (1) gives the following:

`(h,k)=(x,y)=(-4,13)`

Therefore the vertex form of the equation is as follows:

`y=(1)/(2)(x-4)^2+13\Rightarrow(A)`

Therefore the answer is Option(A).