The axis of symmetry is a vertical line at x = -2
The maximum value is -3
Step-by-step explanation:
The vertex form of the equation of the downward parabola is
y = -a(x - h)² + k, where:
- h , k are the coordinates of its vertex
- a is the coefficient of x²
- The axis of symmetry of it is a vertical line passes through the vertex (h , k), and its equation is x = h
- The maximum value is k when x = h
∵ A parabola opens downwards
∴ The vertex form of its equation is y = -a(x - h)² + k
∵ It has a vertex of (-2 , -3)
∵ (h , k) is its vertex
∴ h = -2 and k = -3
Substitute the value of h , k in the form above
∴ y = -a(x - -2)² + -3
∴ y = -a(x + 2)² - 3
∵ The y-intercept is (0 , -11)
- Substitute x by 0 and y by -11 to find a
∵ x = 0 and y = -11
∴ -11 = -a(0 + 2)² - 3
∴ -11 = -a(4) - 3
∴ -11 = -4a - 3
- Add 3 to both sides
∴ -8 = -4a
- Divide both sides by -4
∴ a = 2
Substitute the value of a in the form of the equation
∴ y = -2(x + 2)² - 3 is the equation of the parabola
∵ Its vertex is (-2 , -3)
∵ The axis of symmetry passes through the vertex
∴ The axis of symmetry is a vertical line at x = -2
∵ The maximum value is k when x = h
∵ k = -3
∴ The maximum value is -3
The axis of symmetry is a vertical line at x = -2
The maximum value is -3
Learn more:
You can learn more about the parabola in brainly.com/question/8054589
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