Question 334.
The internal distance of this structure on the page is 8cm and the height on the page is 9cm. Work out a formula which calculates the actual height of the inside edge of this structure (y), in metres at any horizontal distance x measured from the origin point which is the spot where the inside of the left arch touches the ground. Find a formula that matches your data and diagram, in the form y = a(x-h)^2 + k.
Answer 334.
y = a (x - h)^2 + k
=> (y - k) = a (x - h)^2
With the given origin, vertex of the parabola
(h, k) = (4, 9)
=> equation of the parabola is
y = a (x - 4)^2 + 9
Also, (8, 0) is on the parabola
=> 0 = a (8 - 4)^2 + 9
=> a = - 9/16
=> equation of the parabola is
y = - [9/(16)] (x - 4)^2 + 9.
Link to YA!
The internal distance of this structure on the page is 8cm and the height on the page is 9cm. Work out a formula which calculates the actual height of the inside edge of this structure (y), in metres at any horizontal distance x measured from the origin point which is the spot where the inside of the left arch touches the ground. Find a formula that matches your data and diagram, in the form y = a(x-h)^2 + k.
Answer 334.
y = a (x - h)^2 + k
=> (y - k) = a (x - h)^2
With the given origin, vertex of the parabola
(h, k) = (4, 9)
=> equation of the parabola is
y = a (x - 4)^2 + 9
Also, (8, 0) is on the parabola
=> 0 = a (8 - 4)^2 + 9
=> a = - 9/16
=> equation of the parabola is
y = - [9/(16)] (x - 4)^2 + 9.
Link to YA!
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