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Paul [167]
3 years ago
15

Write the equation of the parabola that has the vertex at point (− 1/2 ,2.3) and passes through the point (5,2 3/4 ).

Mathematics
1 answer:
Alex73 [517]3 years ago
5 0

Answer:

The equation of parabola in vertex form is y=0.015(x+0.5)^2+2.3

Step-by-step explanation:

Given coordinate of vertex is (-\frac{1}{2},2.3) and the parabola passes through the point (5,2\frac{3}{4})

So, the equation of parabola in vertex form is

y=a(x-h)^2+k

Where (h,k) is the coordinate of the vertex.

(h,k)=(-\frac{1}{2},2.3)=(-0.5,2.3).\\\\So,\ h=-0.5\ and\ k=2.3

Plugging these value in equation we get,

y=a(x-(-0.5))^2+2.3\\\\y=a(x+0.5)^2+2.3

Now, we will find the value of a

Plug the coordinate (5,2\frac{3}{4})

(x,y)= (5,2\frac{3}{4})\\\\(x,y)=(5,\frac{11}{4})\\\\(x,y)=(5,2.75)

2.75=a(5-(-0.5))^2+2.3\\\\2.75=a(5+(0.5))^2+2.3\\\\2.75=a(5.5)^2+2.3\\\\2.75=a\times30.25+2.3\\\\2.75-2.3=a\times30.25\\\\0.45=a\times30.25\\\\\frac{0.45}{30.25}=a\\ \\a=0.0149

Plug the value of a in the equation y=a(x+0.5)^2+2.3

So, the equation of parabola with vertex (-\frac{1}{2},2.3) and passes through the point (5,2\frac{3}{4}) is

y=0.0149(x+0.5)^2+2.3 ≅y=0.015(x+0.5)^2+2.3

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