Question

Find the vertex: y = −2x^2 + 4x − 3
I already know that the answer is (1, -1) but I can't figure out how to solve it.
This is what I did:
y=ax^2+bx+c so
y = −2x^2 + 4x − 3 is already in standard form.
a=2, b=4, and c=3

x = -b/a = -4/2 = -2
(By now, I already know I must've done something wrong.)

Substitute x back into the equation:
y = −2(-2)^2 + 4(-2) − 3
(2)4 -8 - 3
8 -8 - 3
y= -3

So that means my vertex would be (-2, -3) but I know that it's wrong. Could someone help me figure out how to solve it?

Answer 1

use x = -b/2a not -b/a

Answer 2

-b/a used to find the sum of roots that equation :
x1+x2 = -b/a

Answer 3

a = -2, b=4, and c=-3 not
a =2, b=4, and c=3

Answer 4

But that time I got -5

y = −2x^2 + 4x − 3
a = 2, b = 4, and c = -3

x = -b/2a
-4/2 * 2 = -1

substitute x back into the equation:
y = −2(-1)^2 + 4(-1) − 3
-2(-1) - 4 - 3
2 -7
y = -5

Answer 5

(-1)^2 = 1, not -1

Answer 6

x = -b/2a
x= -4/2 * (-2) = -4/-4 = 1

Answer 7

So then I don't have to substitute x back into the equation?

Answer 8

You get \(1\) for the \(x\)-coordinate, now substitute \(1\) for \(x\) to get the \(y\)-coordinate.

Answer 9

Oh okay, I have it now. Thanks!

Answer 10

NP!

Answer 11

Be careful with the signs... from your earlier post:

y = −2x^2 + 4x − 3
a = 2, b = 4, and c = -3

a = -2 there, not positive 2.

Answer 12

Thanks for pointing that out, I will remember next time :)