Question

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

Answer 1

Answer:

y= 3x^2 - x+5

Step-by-step explanation:

hope that helps

Answer 2

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

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