BONJOURS A TOUS je demnade votre aide sur cette exercice de maths en ANGLAIS s il vous plait ca va etre notee et ma moyenne est horrible c est ma derniere chan

A quadratic function is in the form f(x) = ax^2 + bx +c. A quadratic function graphs into a parabola, Every quadratic function has a vertex and a vertical axis of symmetry.  The vertex point is either the maximum or minimum point for the parabola.

 F(x) = -x^2 -4x+9

The graph opens downward because a is negative.  

The vertex point is at x = -b/2a    

= -(-4)/2*(-1)

= 4/-2

= -2

y = -(-2)^2-4(-2)+9  

= -4+8+9  = 13

Vertex point is at (-2,13)

Axis of symmetry is the equation x = -2

The function has no real roots.  

Solving –x^2-4x+9=0 by Completing the Square

Multiply both sides of the equation by -1:

 (-1)*( –x^2-4x+9) = 0 * (-1)

x^2+4x-9=0

Add 9 to both sides of the equation:

x^2+4x-9+9=0+9

x^2+4x=9

Now take the coefficient of x, which is 4, divide by 2, and finally square it giving 4.

Add 4 to both sides of the equation

: x^2+4x+4 = 9+4

x^2+4x+4 = 13

(x+2)(x+2) = 13

(x+2)^2 = 13

Now take the square root of both sides:

x+2 = √ 13  

x = -2+ √ 13 or x = -2- √ 13  

x Intercepts (Roots):

Root 1 at {x,y} = { 1.61, 0.00}

Root 2 at {x,y} = { -5.61, 0.00}  

Solve the equation x^2-9x-22 = 0 by using the factorized form of the quadratic

Factors of -22 whose sum = -9

-22 + 1 = -21

-2 + 11 = 9

2 – 11 = -9  

Solution:  (x+2)(x-11)