A parabola passes through (0, -1) and (1,1) and is symmetrical about y-axis. How to find the equation of this parabola? Thanks!!

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mitnord wrote:A parabola passes through (0, -1) and (1,1) and is symmetrical about y-axis. How to find the equation of this parabola? Thanks!!

You know that the general equation of a parabola is y = ax

. . . . .-1 = a(0)

. . . . .1 = a(1)

From the first equation, you can find the value of c. Plug this into the second equation to find a relationship between a and c.

Since the parabola is

Plug this third point into the general equation. This will give you a second equation that you can simplify for a relationship between a and b.

If you get stuck, please reply showing how far you have gotten in working through the steps. Thank you!

Hi, thank you for reply!

Following your steps I found that:

-1 = c and

-a = -b

What to do next? I was only given the two points: (0, -1) and (1, 1) and that the parabola is symmetrical around y-axis. Is it even possible?

Following your steps I found that:

-1 = c and

-a = -b

What to do next? I was only given the two points: (0, -1) and (1, 1) and that the parabola is symmetrical around y-axis. Is it even possible?

mitnord wrote:Following your steps I found that:

-1 = c and

-a = -b

What to do next? I was only given the two points: (0, -1) and (1, 1) and that the parabola is symmetrical around y-axis. Is it even possible?

c = -1 is correct, but -a = -b isn't. I think you may have made a mistake when dealing with the sign of c.

From the point (1, 1), x = 1 and y = 1

So, since for a parabola:

y = ax

(1) = a(1)

1 = a + b + c

And from the previous equation, c = -1, so

1 = a + b + (-1) <-- Need to be careful with the minus sign here

1 = a + b - 1

Add 1 to both sides:

1 + 1 = a + b - 1 + 1

2 = a + b

Subtract b from both sides:

2 - b = a + b - b

2 - b = a

So, a = 2 - b

As Eliz has said, the key piece of information to find the

The point (0, -1), where x = 0, lies

However, the point (1,1) does

So, from this information, what will be the coordinates of the reflection of (1,1)? This will be your third point which you can then use as outlined by Eliz above.

DAiv