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lesya [120]
3 years ago
8

Find the equation of the parabola that passes through the points: (0,5) (1,7) (-2,19)

Mathematics
2 answers:
Ymorist [56]3 years ago
3 0

Answer:

y= 3x^2 - x+5

Step-by-step explanation:

hope that helps

Lubov Fominskaja [6]3 years ago
3 0

Answer:

y=3x^{2} -x+5

Step-by-step explanation:

The general form of a parabola is

y=ax^{2} +bx+c

Now, we have three points, where each of them gives values for (x,y). We can use them to create a system of three equations with three unknown variables

5=c\\7=a(1)^{2} +b(1)+c\\19=a(-2)^{2} +b(-2)+c

Then, we replace the value of c in the second and third equation to find create an equation with only two variables

7=a+b+5\\19=4a-2b+5

2=a+b\\14=4a-2b

Then, we multiply the first equation by 2, and sum both equations

4=2a+2b\\14=4a-2b

18=6a\\a=\frac{18}{6}\\ a=3

Finally, we use this value to find b

2=a+b\\2=3+b\\b=2-3\\b=-1

Therefore, the equation of the parabola is

y=ax^{2} +bx+c\\y=3x^{2} -x+5

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