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The hole is 8 feet deep at ground level ⇒ 3rd answer
Step-by-step explanation:
The form of the quadratic function is y = ax² + bx + c, where
- a is the coefficient of x²
- b is the coefficient of x
- c is the y-intercept (at x = 0)
The vertex point of the quadratic is (h , k), where
and k is the value of y when x = h
The table:
→ x : -2 , 0 , 2
→ y : -6 , -8 , -6
∵ x represents distance from hole's center in feet
∵ y represents the depth from level ground
∴ The quadratic function is y = ax² + bx + c
∵ c is the value of y at x = 0 ⇒ y-intercept
- From the table at x = 0 ⇒ y = -8
∴ c = -8
- Substitute its value in the function model
∴ y = ax² + bx - 8
- To find the values of a and b substitute x and y in the model by
the coordinates of the point in the table
∵ x = -2 and y = -6
∴ -6 = a(-2)² + b(-2) - 8
∴ -6 = 4a - 2b - 8
- Add 8 to both sides
∴ 2 = 4a - 2b
- Switch the two sides
∴ 4a - 2b = 2 ⇒ (1)
∵ x = 2 and y = -6
∴ -6 = a(2)² + b(2) - 8
∴ -6 = 4a + 2b - 8
- Add 8 to both sides
∴ 2 = 4a + 2b
- Switch the two sides
∴ 4a + 2b = 2 ⇒ (2)
Now we have a system of equation to solve it
Add equations(1) and (2) to eliminate b
∵ 8a = 4
- Divide both sides by 8
∴ a = 0.5
- Substitute value of a in equation (1) or to to find b
∵ 4(0.5) + 2b = 2
∴ 2 + 2b = 2
- Subtract 2 from both sides
∴ 2b = 0
- Divide both sides by 2
∴ b = 0
Substitute the values of a and b in the function model
∴ y = 0.5x² + (0)x - 8
∴ y = 0.5x² - 8
∵ y represents the depth from level ground
∵ The vertex of the function model is (h , k)
∴ The deep of the hole at ground level is the value of k
∵
∴
∴ h = 0
∵ k is the value of y when x = h
- From the table at x = 0 ⇒ y = -8
∴ k = -8
- Ignore the sign (-) because the k represents the depth of the
hole in feet
∴ The deep of the hole at ground level is 8 feet
The hole is 8 feet deep at ground level
Learn more:
You can learn more about the quadratic function in brainly.com/question/1332667
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