Question

Graphy y=x^ prime 2+3x+2 What are the zeros, the axis of symmetry, and the axordinates of the vertex? Show or explain your work for each

Answer 1

Answer:

a) x=-2 or x=-1

b) x=-1.5

c) (-1.5,-0.25)

Step-by-step explanation:

The given function is

$y = {x}^{2} + 3x + 2$

We complete the square as follows:

$y = {x}^{2} + 3x + 1.5 ^{2} - {1.5}^{2} + 2$

$y = {x}^{2} + 3x + 2.25 - 0.25$

We factor the perfect square;

$y = {(x + 1.5)}^{2} - 0.25$

We obtained the vertex form of the function.

a) To find the zeros, we set y=0.

${(x + 1.5)}^{2} - 0.25 = 0$

${(x + 1.5)}^{2} = 0.25$

$x + 1.5 = \pm \sqrt{0.25}$

$x = - 1.5 \pm 0.5$

$x = - 2 \: or \: x = - 1$

b) The parabola in the form

$y = a( {x - h)}^{2} + k$

has axis of symmetry at x=h.

Comparing this to

$y = ( {x + 1.5)}^{2} - 0.25$

We have

$x = - 1.5$

as the axis of symmetry.

The vertex is (h,k)=(-1.5,-0.25)