The axis of symmetry of the parabola y = -x² + 2x - 7 is at x = 1
Step-by-step explanation:
In the quadratic equation y = ax² + bx + c, where a, b , c are constant
1. It is represented graphically by a parabola
2. The vertex of the parabola is point (h , k)
3. h = [tex]\frac{-b}{2a}[/tex] and k = f(h), where a is the coefficient of x²
and b is the coefficient of x
4. The axis of symmetry of the parabola is a vertical line passes through
the vertex point and its equation is x = h
∵ y = -x² + 2x - 7
∵ y = ax² + bx + c
∴ a = -1 , b = 2 and c = -7
∵ (h , k) are the coordinates of its vertex
∵ h = [tex]\frac{-b}{2a}[/tex]
∴ h = [tex]\frac{-2}{2(-1)}[/tex]
∴ h = 1
∵ k = f(h)
- Substitute x in the equation by 1
∴ k = -(1)² + 2(1) - 7 = -1 + 2 - 7
∴ k = -6
∴ The coordinates of the vertex of the parabola are (1 , -6)
∵ The axis of symmetry of it is a vertical line passes through the
vertex point (1 , -6)
∵ Its equation is x = h
∵ h = 1
∴ The equation of the axis of symmetry is x = 1
The axis of symmetry of the parabola y = -x² + 2x - 7 is at x = 1
Learn more:
You can learn more about parabola in brainly.com/question/8054589
#LearnwithBrainly
