Question

find an equation in standard form of the parabola passing through the points (0, - 1), (1, 5), (- 1, - 5)

Answer 1

The equation of the parabola in standard is
`y=x^(2)+5x-1`

Explanation:

The standard form equation of the parabola is:

`y=ax^(2)+bx+c`

Using the three points we can find a, b and c.

Let's put the first point (0,-1)into the standard form equation.

`-1=a(0)^(2)+b(0)+c`

`c=-1`

Using the second point (1,5) and the value of c found above.

`5=a(1)^(2)+b(1)+c`

`5=a+b-1`

`6=a+b` (1)

Finally using the las point (-1,-5)

`-5=a(-1)^(2)+b(-1)+c`

`-5=a-b-1`

`-4=a-b` (2)

Solving the system of equations (1) and (2) we can find a and b.

`6=a+b`

`-4=a-b`

Adding both of them we have:

`2=2a`

`a=1`

And b = 5.

Therefore, the equation of the parabola in standard form will be.

`y=x^(2)+5x-1`

I hope it helps you!