The vertex of a parabola occurs where the derivative of its equation is 0, so an equation associated with the equation of a parabola can be solved to find the x-coordinate of the vertex. Find the vertex of the parabola, given the equation of the parabola and its associated equation.Equation of parabola: f(x) = 8x2 + 32x - 12; associated equation: 0 = 16x + 32

A. (2, -44)
B. (2, 84)
C. (-2, 84)
D. (-2, -44)


Answer: D

Mathematics

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What will be an ideal response?

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Find the exact acute angle ? for the given function value.sin ? = 

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Use a ruler, protractor, and compass to construct, if possible, a triangle with the stated properties. If such a triangle cannot be drawn, explain why. Decide if there can be two or more noncongruent triangles with the stated properties.A triangle with sides of length 11 cm and 11 cm and a nonincluded angle of 46°

A. Exactly one such triangle can be constructed. B. No such triangle can be constructed. C. Two or more such noncongruent triangles can be constructed.

Mathematics

Find: a. The center and radius of the circle. b. The x- and y-intercepts of the graph of the circle.x2 + y2 + 6 = 0

A. a. center = (0, 0); radius = 6
b. (-, 0), (, 0), (0, ), (0, -)
B. a. center = (0, 0); radius = 
b. (, 0), (0, )
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D. a. ?
b. ?

Mathematics