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)
