The equation of the parabola is y = -1.5(x + 8)² + 4 in the vertex form
Step-by-step explanation:
The equation of the parabola in the vertex form is y = a(x - h)² + k
where
1. (h , k) are the coordinates of its vertex point
2. x and y are the coordinates of a general point on the parabola
∵ The equation of the parabola is y = a(x - h)² + k
∵ The vertex of the parabola is (-8 , 4)
∴ h = -8 and k = 4
∵ The parabola passes through point (-6 , -2)
∴ x = -6 and y = -2
- Substitute these values in the equation above to find value of a
∴ -2 = a(-6 - -8)² + 4
∴ -2 = a(-6 + 8)² + 4
∴ -2 = a(2)² + 4
∴ -2 = 4a + 4
- Subtract 4 from both sides
∴ -6 = 4a
- Divide both sides by 4
∴ a = -1.5
∴ The equation of the parabola in the vertex form is:
y = -1.5(x + 8)² + 4
The equation of the parabola is y = -1.5(x + 8)² + 4 in the vertex form
Learn more:
You can learn more about the parabola in brainly.com/question/9390381
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