Answer:
The equation of the parabola in standard is [tex]y=x^{2}+5x-1[/tex]
Step-by-step explanation:
The standard form equation of the parabola is:
[tex]y=ax^{2}+bx+c[/tex]
Using the three points we can find a, b and c.
Let's put the first point (0,-1)into the standard form equation.
[tex]-1=a(0)^{2}+b(0)+c[/tex]
[tex]c=-1[/tex]
Using the second point (1,5) and the value of c found above.
[tex]5=a(1)^{2}+b(1)+c[/tex]
[tex]5=a+b-1[/tex]
[tex]6=a+b[/tex] (1)
Finally using the las point (-1,-5)
[tex]-5=a(-1)^{2}+b(-1)+c[/tex]
[tex]-5=a-b-1[/tex]
[tex]-4=a-b[/tex] (2)
Solving the system of equations (1) and (2) we can find a and b.
[tex]6=a+b[/tex]
[tex]-4=a-b[/tex]
Adding both of them we have:
[tex]2=2a[/tex]
[tex]a=1[/tex]
And b = 5.
Therefore, the equation of the parabola in standard form will be.
[tex]y=x^{2}+5x-1[/tex]
I hope it helps you!
