Question

[9.01] The graph of which equation is shown below?

a u-shaped graph on a coordinate plane that is opening up and has a vertex of (2, −3)

y = x2 − 4x + 1

y = x2 + 4x + 1

y = −x2 − 4x + 1

y = −x2 + 4x + 1

Answer 1

this is the graph

Answer 2

help me please

Answer 3

it is the graph of
y = x2 − 4x + 1
y+3=x2 − 4x + 1+3
or y+3=(x-2)^2

Answer 4

wht?

Answer 5

please help me please

Answer 6

@Hero @phi @agent0smith can someone please help me w/this

Answer 7

A month-old question? D:

Answer 8

Yea I have the same question on an online course

Answer 9

Which isn't even yours? :3
anyway, check the vertices of each of the answer choices... If you have an equation of the form
\[\Large y =\color{blue}ax^2 + \color{red}bx + \color{green}c\]
Then the vertex of its graph is given by
\[\huge \left(-\frac{\color{red}b}{2\color{blue}a}\qquad,\qquad\frac{4\color{blue}a\color{green}c-\color{red}b^2}{4\color{blue}a}\right)\]

Answer 10

But it's opening upward, so that \(\large x^2\) coefficient MUST be positive, so that rules out choices C and D (since they both have \(\large -x^2\))

Answer 11

so it's B because the 4 is positive?

Answer 12

I don't actually know... so you know choice B opens upward, that's good.
But what's the vertex of choice B?
Use this formula:
\[\huge \left(-\frac{\color{red}b}{2\color{blue}a}\qquad,\qquad\frac{4\color{blue}a\color{green}c-\color{red}b^2}{4\color{blue}a}\right)\]

Answer 13

\[\Large y = x^2 + 4x + 1 = \color{blue}1x^2 + \color{red}4x+\color{green}{1}\]

Answer 14

so x=-2

Answer 15

Yup... but you want the vertex to be (2,-3) so...?

Answer 16

and the second equation is -4 I think

Answer 17

It isn't, but anyway, the first coordinate, -b/2a gives you -2.

But the vertex that you want is (2,-3)

Answer 18

y=-3

Answer 19

how do I change x to positive

Answer 20

LOL You don't ^_^
You just figured out (though you seem to not know) the vertex of the choice B
Which is x = -2, y = -3

Or (-2,-3)

But that's something you can't change... the vertex of the second equation IS (-2,-3) which means it isn't the equation you're looking for :P

Answer 21

So it's A

Answer 22

By process of elimination, it must be :)
Though you'd do well to apply the vertex formula to choice A
\[\huge \left(-\frac{\color{red}b}{2\color{blue}a}\qquad,\qquad\frac{4\color{blue}a\color{green}c-\color{red}b^2}{4\color{blue}a}\right)\]
Just to assure yourself that it IS the correct answer :)

Answer 23

And that you SHOULD get the vertex x = 2 and y = -3
(2 , -3)

Cheers ^_^

Answer 24

Thanks so much

Answer 25

Don't forget why choices C and D were not considered, okay?
The question says the graph opens upward, and this is determined solely by the sign of the \(\large x^2\) term... if it's positive, as in choices A and B, the graph opens up, and if it's negative, as in choices C and D, the graph opens down ^_^