Which describes the cross section of the square prism that passes through the vertices A, B, C, and D shown below?
2 answers:
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Answer:
(- 5, 0 ), (7, 0 )
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (1, - 108 ), thus
y = a(x - 1)² - 108
To find a substitute (0, - 105 ) into the equation
- 105 = a(- 1)² - 108 ( add 108 to both sides )
3 = a
y = 3(x - 1)² - 108 ← equation in vertex form
To find the x- intercepts, let y = 0, that is
3(x - 1)² - 108 = 0 ( add 108 to both sides )
3(x - 1)² = 108 ( divide both sides by 3 )
(x - 1)² = 36 ( take the square root of both sides )
x - 1 = ± = ± 6 ( add 1 to both sides )
x = 1 ± 6, so
x = 1 - 6 = - 5
x = 1 + 6 = 7
x- intercepts are (- 5, 0), (7, 0)