Graph the function using it vertex, axis of symmetry and intercepts f(x)=x^2+6x+9

Question

please help!

Answer 1

Given f(x) = x^2+6x+9

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

a = 1, b = 6, c = 9

Axis of symmetry is x = -b/2a = -6/2*1 = -3

→ Axis of symmetry is x = -3.

Substitute x = -3 in given equation y = (-3)^2+6(-3)+9

y = 9-18+9

y = 0

→ Vertex of parabola is (x,y) = (-3,0)

To fnd y intercept substitute x = 0 in given equation.

y = x^2+6x+9 = 0+0+9 = 9

→ y intercept is 9.

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

0 = x^2+6x+9

x^2+3x+3x+9 = 0

x(x+3)+3(x+3) = 0

(x+3)(x+3) = 0

x+3 = 0 and x+3 = 0

x = -3 and x = -3

→ x intercept is -3.

Graph of parabola

Draw the coordinate plane.

plot the vertex of parabola and x intercepts and y intercepts.

Connect the points neatly ,sensitively like a curve.

Then ther is formed required parabola.

 

 

Answer 2

The function f (x ) = x ² + 6x  + 9

y  = x ² + 6x + 9

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

a  = 1, b  = 6, c  = 9

Axis of symmetry x  = -b /2a  = -6/2

Axis of symmetry x  = -3

Substitute x  value in y  = x ² + 6x  + 9

y  = (-3)² + 6(-3) + 9

y  = 0

Vertex of parabola (x , y ) = (-3, 0)

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

0  = x ² + 6x  + 9

(x + 3)²  = 0

x + 3 = 0

x = -3

So x  intercept is (-3, 0).

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

 y  = (0) ² + 6(0)  + 9

y  = 9

So y  intercept is (0, 9).

Graph

1.Draw the coordinate plane.

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

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