The axis of symmetry is x = 6
Further explanation
Discriminant of quadratic equation ( ax² + bx + c = 0 ) could be calculated by using :
D = b² - 4 a c
From the value of Discriminant , we know how many solutions the equation has by condition :
D < 0 → No Real Roots
D = 0 → One Real Root
D > 0 → Two Real Roots
Let us now tackle the problem!
An axis of symmetry of quadratic equation y = ax² + bx + c is :
[tex]\large {\boxed {x = \frac{-b}{2a} } }[/tex]
Given:
[tex]f(x) = - (x + 9)(x - 21)[/tex]
[tex]f(x) = - (x^2 - 21x + 9x - 189)[/tex]
[tex]f(x) = - (x^2 - 12x - 189)[/tex]
[tex]f(x) = -x^2 + 12x + 189[/tex]
The axis of symmetry is
[tex]x = \frac{-b}{2a}[/tex]
[tex]x = \frac{-12}{2(-1)}[/tex]
[tex]x = \frac{-12}{-2}[/tex]
[tex]\large {\boxed {x = 6} }[/tex]
Learn more
- Solving Quadratic Equations by Factoring : https://brainly.com/question/12182022
- Determine the Discriminant : https://brainly.com/question/4600943
- Formula of Quadratic Equations : https://brainly.com/question/3776858
Answer details
Grade: High School
Subject: Mathematics
Chapter: Quadratic Equations
Keywords: Quadratic , Equation , Discriminant , Real , Number , Axis , Symmetry , Function
