A parabola has its maximum at (4, 8) and an x–intercept at x = –2.
1 answer:
The other x-intercept is at x = 10
Step-by-step explanation:
The vertex form of the parabola is y = a(x - h)² + k, where
- (h , k) are the coordinates of the vertex point of the parabola
- a is the leading coefficient of the equation of the parabola
- If a < 0 , then the vertex point is maximum
- If a > 0 , the the vertex point is minimum
∵ The parabola has a maximum point at (4 , 8)
∴ h = 4 and k = 8
∵ The form of the equation of the parabola is y = a(x - h)² + k
∴ The equation of the parabola is y = a(x - 4)² + 8
∵ The x-intercept is at x = -2
- x-intercept means the parabola intersects the x-axis at point (-2 , 0)
∵ x = -2 and y = 0
- Substitute these values in the equation above to find a
∴ 0 = a(-2 - 4)² + 8
∴ 0 = a(-6)² + 8
∴ 0 = 36 a + 8
- Subtract 36 a from both sides
∴ -36 a = 8
- Divide both sides by -36
∴ a =
∴ The equation of the parabola is y = (x - 4)² + 8
To find the other x-intercept substitute y by 0
∵ 0 = (x - 4)² + 8
- Subtract 8 from both sides
∴ -8 = (x - 4)²
- Divide both sides by
∴ 36 = (x - 4)²
- Take √ for both sides
∴ x - 4 = 6 or x - 4 = -6
- Add 4 to both sides
∴ x = 10 or x = -2
The other x-intercept is at x = 10
Learn more:
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