how don you graph and find the vertex.....

Question

Find:

y=x²+4x+4

a) Vertex

b)axis of symmetry

c)X-intercept and y-intercept

d)graph

Answer 1

Given equation y = x^2+4x+4

Compare it to parabola standard equation y = ax^2+bx+c

a = 1,b = 4, c = 4

b) Axis of symmetry x = -b/2a = -4/2*1

x = -2

a) To find vertex substitute the x value in given equation.

y = (-2)^2+4(-2)+4

y = 4-8+4

y = 0

Vertex of parabola is (x,y) = (-2,0)

c) To find y intercept substitute y = 0 in given equation.

y = 0^2+4*0+4

y intercept is  4

To find x intercept substitute x = 0 in given equation.

0 = x^2+4x+4

x^2+2x+2x+4 = 0

x(x+2)+2(x+4) = 0

(x+2)(x+4) = 0

x = -2,y = -4

X intercepts are -2,-4.

d)graph of the parabola

Comments

Check your solution ..

c)x  intercept is -2.

Answer 2

 y  = x ² + 4x + 4

The above equation represent a standard form of parabola y  = ax ² + bx + c .

a  = 1, b  = 4, c  = 4

Axis of symmetry x  = -b /2a  = -4/2

b)Axis of symmetry x  = -2

Substitute x  value in y  = x ² + 4x  + 4

y  = (-2)² + 4(-2) + 4

y  = 0

a)Vertex of parabola (x , y ) = (-2, 0)

c)To find intercepts of parabola

To find x intercept substitute y  = 0 in y  = x ² + 4x  + 4.

0  = x ² + 4x  + 4

(x + 2)²  = 0

x + 2 = 0

x = -2

So x  intercept is (-2, 0).

To find y  intercept substitute x = 0 in y  = x ² + 6x  + 9.

 y  = (0) ² + 4(0)  + 4

y  = 4

So y  intercept is (0, 4).

Choose values for x and find the corresponding values for y.

x	y  = x 2 + 4x  + 4	(x, y)
-1	y = (-1)2 + 4(-1)+4 y = 1	(-1,1)
-3	y = (-3)2+ 4(-3)+ 4  y = 1	(-3,1)
-4	y = (-4)2 + 4(-4)+4   y = 4	(-4,4)

d)Graph

1.Draw the coordinate plane.

2.Plot the vertex , axis of symmetry and x , y  intercepts of parabola.

3.Plot the points found in the table.

4.Then sketch the graph, connecting the points with a smooth curve.