Question

how do you solve a parabola? y=x^2-4x+3
i know you find the intercepts, y=3 and x=3, 1.
but what next?

Answer 1

what do you want done? what do you mean to "solve a parabola"?

Answer 2

like, graph a parabola... i think

Answer 3

you want to find the axis of symmetry and the vertex

Answer 4

how do i do that?

Answer 5

in the form
\[ax^2+bx+c\]
the axis of symmetry is
\[x=\frac{-b}{2a}\]
the vertex is
\[(\frac{-b}{2a}, f(\frac{-b}{2a}))\]

Answer 6

so y=x^2-4x+3 would become x=4/2?
for the axis of symmetry

Answer 7

and for the vertex it would be 4/2 times f(4/2)?
what does the f mean?

Answer 8

as in f(x)
plug in -b/(2a) into the equation of the parabola to get the y-coordinate

Answer 9

so vertex is at (2, -1)

Answer 10

it is a point

Answer 11

put 4/2 (-b/2a) where f(x) is?

Answer 12

no..
f(x)=x^2-4x+3
this is the equation of your parabola
the axis of symmetry is the vertical line that passes through the x-coordinate of your vertex
To get the y-coordinate, plug in the x-coordinate into f(x)
so f(2)=-1

Answer 13

where'd you get f(2)=-1?

Answer 14

plug 2 into f(x)
f(2)=2^2-4(2)+3=4-8+3=-1

Answer 15

oh ok
alright so the f(4/2) = 2^2-4(2)+3
so f(2) = 4-8 +3
so f(2) = -1. alright, so that's the y coordinate?

Answer 16

yes, the y-coordinate of the vertex
the vertex is the point (2,-1)

Answer 17

ok. so let me just review here. the x coordinate to the vertex is -b/2a, which we then plug in for f(x) and solve for the y coordinate. where do the two side points come from?

Answer 18

what 2 side points?

Answer 19

the vertex is the middle one, but there have to be two other points, don't there?
it's not a parabola with one point

Answer 20

there are an infinite number of points on a parabola, not just 3

Answer 21

you want the x-intercepts, the y-intercept, the vertex, and the axis of symmetry. a few other points won't hurt either

Answer 22

yeah, but you are only require to graph 3... so where do i get the other 2? :o

Answer 23

you already found the x-intercepts, (3, 0) and (1, 0)

Answer 24

the y-intercept is (0, 3) not y=3

Answer 25

ohhhh ok. so the three points are (3,0), (1,0), and (2, -1)

Answer 26

you could use those, i'd also use a 4th point for the y-intercept of (0,3)

Answer 27

oh ok. thank you sooooo much. you're a life saver!

Answer 28

yw