helppp!!!!

Question

draw an accurate graph of the quadratic function y= 4x^2 + 8x + 4 on the grid below. FIll in the table of values forr five critical points including the vertwx,x intercepts,y intercepts and other points that show the symmetry for the grap. then answer below :

a) How many solution are there for the quadratic equation 4x + 8x + 4 = 0? how do you know this by looking at the graph?

Thanks

Answer 1

The quadratic function y = 4x² + 8x + 4

Compare it to y = ax² + bx + c

a = 4, b = 8, c = 4

Axis of symmetry x = -b/2a

x = -8/2(4) = -8/8

Axis of symmetry x = -1

 

To find vertex substitute x = - 1 in y = 4x² + 8x + 4.

y = 4(-1)² + 8(-1) + 4

y = 4 - 8 + 4

y = 0

Vertex (x, y) = (-1, 0).

 

To find x intercepts substitute y = 0 in y = 4x² + 8x + 4.

0 = 4x² + 8x + 4

x² + 2x + 1 = 0

(x + 1)² = 0

x + 1 = 0

x  = -1

x intercept is  (-1, 0)

 

To find y intercepts substitute x = 0 in y = 4x² + 8x + 4.

y = 4(0)² + 8(0) + 4

y = 4

y intercept is  (0, 4)

Make the table of values to find ordered pairs that satisfy the equation.

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

x	y = 4x2 + 8x + 4	(x, y)
- 2	y = 4(-2)2 + 8(-2) + 4 = 4	(- 2, 4)
-1.5	y = 4(-1.5)2 + 8(-1.5) + 4 = 1	(-1.5, 1)
-0.5	y = 4(-0.5)2 + 8(-0.5) + 4 = 1	(-0.5, 1)
-1	y = 4(-1)2 + 8(-1) + 4 = 1	(-1, 0)
0	y = 4(0)2 + 8(0) + 4 = 4	(0, 4)

 

Comments

Contd...

Graph

Draw the coordinate plane.

Plot the points found in the table.

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

Connect the plotted points with smooth curve.

a) The equation 4x² + 8x + 4 = 0 have one solution at x  = - 1.

x intercepts are solutions of quadratic function.

From the graph x intercept is - 1.