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Select the correct answer.What is the equation of the parabola shown with its focus on this graph?

Select the correct answer.What is the equation of the parabola shown with its focus-example-1
User JG In SD
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1 Answer

2 votes

Solution:

Given:

From the graph, the vertex is at (0,1)

Using the equation of a parabola in vertex form;


\begin{gathered} y=a(x-h)^2+k \\ where; \\ (h,k)=(0,1) \\ h=0 \\ k=1 \\ \\ Hence, \\ y=a(x-0)^2+1 \\ y=ax^2+1 \end{gathered}

To get the constant a,


\begin{gathered} Using\text{ the point }(7,-3) \\ x=7 \\ y=-3 \\ \\ y=ax^2+1 \\ -3=a(5^2)+1 \\ -3-1=49a \\ -4=49a \\ -(4)/(49)=a \\ a\approx-(1)/(12) \end{gathered}

Hence, the equation is;


y=-(1)/(12)x^2+1

The graph is shown;

Therefore, option A is correct.

Select the correct answer.What is the equation of the parabola shown with its focus-example-1
Select the correct answer.What is the equation of the parabola shown with its focus-example-2
User Pierre Chambart
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