Question

Help please
Determine the direction that this parabola opens y=2x^2-4x+5
Up or down?

Answer 1

Hi there!

It's an up parabola

Answer 2

How do you know though?

Answer 3

I can write the equation as:

\[y = 2(x^2 - 2x + 1) + 3 = 2 (x-1)^2 + 3\]

Now, look closely on the RHS:

\((x-1)^2\) will always be positive

As the value of x increases, y also increases. That's why, you have an up parabola

Answer 4

Ah okay. Thank-you very much

Answer 5

Your welcome!

Cheers!

Answer 6

So would y=-2x^2-8x-15 be down?

Answer 7

You got it right!

Answer 8

Thank-you for helping me understand

Answer 9

(y) Your welcome :)