Question

Help in the process of graphing
y = x^2 + 5x + 2

Answer 1

@phi

Answer 2

what kind of curve is this ? any idea ?

Answer 3

Parabola

Answer 4

yes. any idea what the x value of the vertex is ?
a x^2 + bx + c
x value of vertex is at -b/(2a)

Answer 5

\[\frac{ -b }{ 2a } = \frac{ -5 }{ 2(1) } = \frac{ -5 }{ 2} = -2.5 \]

Answer 6

ok, and you can find the corresponding y value, right ?

Answer 7

yes
\[y= -2.5^2 + 5(-2.5) + 2 = -4.25 \]

Answer 8

ok, so the vertex is at (-2.5, -4.25)

next, is this a smile or frown shape ?

Answer 9

smile?

Answer 10

yes. You know because as you move away from x= 2.5 the parabola gets bigger (goes up)
\( \cup\)
shape

Answer 11

we should find a few points. at x=0 y=2
(0,2)

at x=1 : y= 1+5*1+2= 7

and a few points to the left of -2.5
say at x= -3 and x= -4

Answer 12

we could find where y is 0, but we will get ugly numbers
(we would use the quadratic formula to solve
x^2 + 5x + 2 =0
(or complete the square)
but it seems easier to find a few nice points, plot them, and sketch in the curve.

Answer 13

hmmm, I should add correctly
at x=1 : y= 1+5*1+2= 8

Answer 14

if i plot x = -3 then whatever get will be reflected wth -1 ?

Answer 15

I am not sure what you are asking.

but the y value at x=-3 will also be the y value "on the other side" of the vertex
the vertex is at -2.5
-3 is 0.5 to the left, so you will also know the y value 0.5 to the right, at x= -2

Answer 16

i got it thanks!

Answer 17

Here is a graph (from geogebra) with some of the points:
you can see the symmetry that helps to plot other points.