The equation of the parabola is y = 2x²+2x+3 if the points (-1,3),(0.5,4.5) and (0,3) belong to it.
What is a parabola?
It is defined as the graph of a quadratic function that has something bowl-shaped.
Let's assume the equation of the parabola is:
[tex]\rm y = ax^2+bx+c[/tex]
The points (-1,3), (0.5,4.5) and (0,3) belong to it.
Putting these points in the parabola equation, we get:
[tex]\rm 3 = a(-1)^2+b(-1)+c\\\\\rm a-b+c = 3 \ .....(1)[/tex]
[tex]\rm 0.25a+0.5b+c = 4.5[/tex] ....(2)
[tex]\rm c = 3[/tex] ....(3)
The above shows a linear equation in three variables after solving, we get:
a = 2, b = 2, and z = 3
[tex]\rm y = 2x^2+2x+3[/tex]
Thus, the equation of the parabola is y = 2x²+2x+3 if the points (-1,3),(0.5,4.5) and (0,3) belong to it.
Know more about the parabola here:
brainly.com/question/8708520
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